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Journal articles on the topic 'Srinivasa Ramanujan'

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Published: 4 June 2021

Last updated: 5 February 2022

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1

Alladi, Krishnaswami. "Ramanujan's legacy: the work of the SASTRA prize winners." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 378, no. 2163 (December 9, 2019): 20180438. http://dx.doi.org/10.1098/rsta.2018.0438.

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The SASTRA Ramanujan Prize is an annual $10 000 prize given to mathematicians not exceeding the age of 32 for revolutionary contributions to areas influenced by Srinivasa Ramanujan. The prize has been unusually successful in recognizing highly gifted mathematicians at an early stage of their careers who have gone on to shape the development of mathematics. We describe the fundamental contributions of the winners and the impact they have had on current research. Several aspects of the work of the awardees either stem from or have been strongly influenced by Ramanujan's ideas. This article is part of a discussion meeting issue ‘Srinivasa Ramanujan: in celebration of the centenary of his election as FRS’.

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Andrews, George E. "How Ramanujan may have discovered the mock theta functions." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 378, no. 2163 (December 9, 2019): 20180436. http://dx.doi.org/10.1098/rsta.2018.0436.

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Mock theta functions appeared out of the blue in Ramanujan's last letter to Hardy. What would lead Ramanujan to consider the possibility of such functions in the first place? This paper seeks to provide a plausible answer to this question. This article is part of a discussion meeting issue ‘Srinivasa Ramanujan: in celebration of the centenary of his election as FRS’.

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Vaidyanathan, Palghat P., and Srikanth Tenneti. "Srinivasa Ramanujan and signal-processing problems." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 378, no. 2163 (December 9, 2019): 20180446. http://dx.doi.org/10.1098/rsta.2018.0446.

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The Ramanujan sum c q ( n ) has been used by mathematicians to derive many important infinite series expansions for arithmetic-functions in number theory. Interestingly, this sum has many properties which are attractive from the point of view of digital signal processing. One of these is that c q ( n ) is periodic with period q , and another is that it is always integer-valued in spite of the presence of complex roots of unity in the definition. Engineers and physicists have in the past used the Ramanujan-sum to extract periodicity information from signals. In recent years, this idea has been developed further by introducing the concept of Ramanujan-subspaces. Based on this, Ramanujan dictionaries and filter banks have been developed, which are very useful to identify integer-valued periods in possibly complex-valued signals. This paper gives an overview of these developments from the view point of signal processing. This article is part of a discussion meeting issue ‘Srinivasa Ramanujan: in celebration of the centenary of his election as FRS’.

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Gillman, Nate, Xavier Gonzalez, Ken Ono, Larry Rolen, and Matthew Schoenbauer. "From partitions to Hodge numbers of Hilbert schemes of surfaces." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 378, no. 2163 (December 9, 2019): 20180435. http://dx.doi.org/10.1098/rsta.2018.0435.

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We celebrate the 100th anniversary of Srinivasa Ramanujan's election as a Fellow of the Royal Society, which was largely based on his work with G. H. Hardy on the asymptotic properties of the partition function. After recalling this revolutionary work, marking the birth of the ‘circle method’, we present a contemporary example of its legacy in topology. We deduce the equidistribution of Hodge numbers for Hilbert schemes of suitable smooth projective surfaces. This article is part of a discussion meeting issue ‘Srinivasa Ramanujan: in celebration of the centenary of his election as FRS’.

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Harvey, Jeffrey A. "Ramanujan's influence on string theory, black holes and moonshine." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 378, no. 2163 (December 9, 2019): 20180440. http://dx.doi.org/10.1098/rsta.2018.0440.

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Ramanujan influenced many areas of mathematics, but his work on q -series, on the growth of coefficients of modular forms and on mock modular forms stands out for its depth and breadth of applications. I will give a brief overview of how this part of Ramanujan's work has influenced physics with an emphasis on applications to string theory, counting of black hole states and moonshine. This paper contains the material from my presentation at the meeting celebrating the centenary of Ramanujan's election as FRS and adds some additional material on black hole entropy and the AdS/CFT correspondence. This article is part of a discussion meeting issue ‘Srinivasa Ramanujan: in celebration of the centenary of his election as FRS’.

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Lubotzky, Alexander, and Ori Parzanchevski. "From Ramanujan graphs to Ramanujan complexes." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 378, no. 2163 (December 9, 2019): 20180445. http://dx.doi.org/10.1098/rsta.2018.0445.

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Ramanujan graphs are graphs whose spectrum is bounded optimally. Such graphs have found numerous applications in combinatorics and computer science. In recent years, a high-dimensional theory has emerged. In this paper, these developments are surveyed. After explaining their connection to the Ramanujan conjecture, we will present some old and new results with an emphasis on random walks on these discrete objects and on the Euclidean spheres. The latter lead to ‘golden gates’ which are of importance in quantum computation. This article is part of a discussion meeting issue ‘Srinivasa Ramanujan: in celebration of the centenary of his election as FRS’.

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Debnath, Lokenath. "Srinivasa Ramanujan (1887-1920) and the theory of partitions of numbers and statistical mechanics a centennial tribute." International Journal of Mathematics and Mathematical Sciences 10, no. 4 (1987): 625–40. http://dx.doi.org/10.1155/s0161171287000772.

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This centennial tribute commemorates Ramanujan the Mathematician and Ramanujan the Man. A brief account of his life, career, and remarkable mathematical contributions is given to describe the gifted talent of Srinivasa Ramanujan. As an example of his creativity in mathematics, some of his work on the theory of partition of numbers has been presented with its application to statistical mechanics.

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Winnie Li, Wen-Ching. "The Ramanujan conjecture and its applications." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 378, no. 2163 (December 9, 2019): 20180441. http://dx.doi.org/10.1098/rsta.2018.0441.

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In this paper, we review the Ramanujan conjecture in classical and modern settings and explain its various applications in computer science, including the explicit constructions of the spectrally extremal combinatorial objects, called Ramanujan graphs and Ramanujan complexes, points uniformly distributed on spheres, and Golden-Gate Sets in quantum computing. The connection between Ramanujan graphs/complexes and their zeta functions satisfying the Riemann hypothesis is also discussed. This article is part of a discussion meeting issue ‘Srinivasa Ramanujan: in celebration of the centenary of his election as FRS’.

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Ramachandra, K., and A. Sankaranarayanan. "On an asymptotic formula of Srinivasa Ramanujan." Acta Arithmetica 109, no. 4 (2003): 349–57. http://dx.doi.org/10.4064/aa109-4-5.

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Debnath, Lokenath. "Srinivasa Ramanujan (1887‐1920) A centennial tribute." International Journal of Mathematical Education in Science and Technology 18, no. 6 (November 1987): 821–61. http://dx.doi.org/10.1080/0020739870180608.

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Ravichandran, V. "88.10 On a series considered by Srinivasa Ramanujan." Mathematical Gazette 88, no. 511 (March 2004): 105–10. http://dx.doi.org/10.1017/s0025557200174364.

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12

Alladi, Krishnaswami. "Srinivasa Ramanujan: Going Strong at 125, Part I." Notices of the American Mathematical Society 59, no. 11 (December 1, 2012): 1522. http://dx.doi.org/10.1090/noti917.

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Alladi, Krishnaswami, Ken Ono, K. Soundararajan, R. C. Vaughan, and S. Ole Warnaar. "Srinivasa Ramanujan: Going Strong at 125, Part II." Notices of the American Mathematical Society 60, no. 01 (January 1, 2013): 10. http://dx.doi.org/10.1090/noti926.

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14

Krishnamurthy, Mangala. "The Life and Lasting Influence of Srinivasa Ramanujan." Science & Technology Libraries 31, no. 2 (April 2012): 230–41. http://dx.doi.org/10.1080/0194262x.2012.676901.

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Bhattacharjee, Nil Ratan, and Sabuj Das. "ON GENERALIGATIONS OF PARTITION FUNCTIONS." International Journal of Research -GRANTHAALAYAH 3, no. 10 (October 31, 2015): 1–29. http://dx.doi.org/10.29121/granthaalayah.v3.i10.2015.2928.

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In 1742, Leonhard Euler invented the generating function for P(n). Godfrey Harold Hardy said Srinivasa Ramanujan was the first, and up to now the only, Mathematician to discover any such properties of P(n). In 1916, Ramanujan defined the generating functions for X(n),Y(n) . In 2014, Sabuj developed the generating functions for . In 2005, George E. Andrews found the generating functions for In 1916, Ramanujan showed the generating functions for , , and . This article shows how to prove the Theorems with the help of various auxiliary functions collected from Ramanujan’s Lost Notebook. In 1967, George E. Andrews defined the generating functions for P1r (n) and P2r (n). In this article these generating functions are discussed elaborately. This article shows how to prove the theorem P2r (n) = P3r (n) with a numerical example when n = 9 and r = 2. In 1995, Fokkink, Fokkink and Wang defined the in terms of , where is the smallest part of partition . In 2013, Andrews, Garvan and Liang extended the FFW-function and defined the generating function for FFW (z, n) in differnt way.

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Sujatha, Ramdorai. "Selmer groups in Iwasawa theory and congruences." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 378, no. 2163 (December 9, 2019): 20180442. http://dx.doi.org/10.1098/rsta.2018.0442.

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This article outlines the behaviour of Iwasawa μ -invariants for Selmer groups of elliptic curves when the residual representations are equivalent. This article is part of a discussion meeting issue ‘Srinivasa Ramanujan: in celebration of the centenary of his election as FRS’.

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Qureshi, Mohammad Idris, and Showkat Ahmad Dar. "Generalizations and applications of Srinivasa Ramanujan’s integral associated with infinite Fourier sine transforms in terms of Meijer’s G-function." Analysis 41, no. 3 (May 19, 2021): 145–53. http://dx.doi.org/10.1515/anly-2018-0067.

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Abstract In this paper, we obtain analytical solutions of an unsolved integral 𝐑 S ⁢ ( m , n ) {\mathbf{R}_{S}(m,n)} of Srinivasa Ramanujan [S. Ramanujan, Some definite integrals connected with Gauss’s sums, Mess. Math. 44 1915, 75–86] with suitable convergence conditions in terms of Meijer’s G-function of one variable, by using Mellin–Barnes type contour integral representations of the sine function, Laplace transform method and some algebraic properties of Pochhammer’s symbol. Also, we have given some generalizations of Ramanujan’s integral 𝐑 S ⁢ ( m , n ) {\mathbf{R}_{S}(m,n)} in the form of integrals ℧ S * ⁢ ( υ , b , c , λ , y ) {\mho_{S}^{*}(\upsilon,b,c,\lambda,y)} , Ξ S ⁢ ( υ , b , c , λ , y ) {\Xi_{S}(\upsilon,b,c,\lambda,y)} , ∇ S ⁡ ( υ , b , c , λ , y ) {\nabla_{S}(\upsilon,b,c,\lambda,y)} and ℧ S ⁢ ( υ , b , λ , y ) {\mho_{S}(\upsilon,b,\lambda,y)} with suitable convergence conditions and solved them in terms of Meijer’s G-functions. Moreover, as applications of Ramanujan’s integral 𝐑 S ⁢ ( m , n ) {\mathbf{R}_{S}(m,n)} , the three new infinite summation formulas associated with Meijer’s G-function are obtained.

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18

Srivatsa, Kumar, and S. Shruthi. "New modular equations of signature three in the spirit of Ramanujan." Filomat 34, no. 9 (2020): 2847–68. http://dx.doi.org/10.2298/fil2009847s.

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Srinivasa Ramanujan recorded many modular equations in his notebooks, which are useful in the computation of class invariants, continued fractions and the values of theta functions. In this paper, we prove some new modular equations of signature three by using theta function identities of composite degrees.

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19

Rankin, R. A., S. Raghavan, and S. S. Rangachari. "Srinivasa Ramanujan: The Lost Notebook and Other Unpublished Papers." Mathematical Gazette 73, no. 465 (October 1989): 276. http://dx.doi.org/10.2307/3618499.

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20

Cheng, Miranda C. N., Francesca Ferrari, and Gabriele Sgroi. "Three-manifold quantum invariants and mock theta functions." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 378, no. 2163 (December 9, 2019): 20180439. http://dx.doi.org/10.1098/rsta.2018.0439.

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Mock modular forms have found applications in numerous branches of mathematical sciences since they were first introduced by Ramanujan nearly a century ago. In this proceeding, we highlight a new area where mock modular forms start to play an important role, namely the study of three-manifold invariants. For a certain class of Seifert three-manifolds, we describe a conjecture on the mock modular properties of a recently proposed quantum invariant. As an illustration, we include concrete computations for a specific three-manifold, the Brieskorn sphere Σ (2, 3, 7). This article is part of a discussion meeting issue ‘Srinivasa Ramanujan: in celebration of the centenary of his election as FRS’.

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Soundararajan, K. "Integral factorial ratios: irreducible examples with height larger than 1." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 378, no. 2163 (December 9, 2019): 20180444. http://dx.doi.org/10.1098/rsta.2018.0444.

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This paper gives over 50 new examples of two-parameter families of integral factorial ratios of height 2. These examples are also shown to be irreducible, in the sense that they do not arise by putting together two factorial ratios of height 1. This article is part of a discussion meeting issue ‘Srinivasa Ramanujan: in celebration of the centenary of his election as FRS’.

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Bhattacharjee, Nil Ratan, and Sabuj Das. "GENERALIZATIONS OF RAMANUJAN’S RANK FUNCTIONS COLLECTED FROM RAMANUJAN’S LOST NOTEBOOK." International Journal of Research -GRANTHAALAYAH 4, no. 3 (March 31, 2016): 1–20. http://dx.doi.org/10.29121/granthaalayah.v4.i3.2016.2780.

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In1916, Srinivasa Ramanujan defined the Mock Theta functions in his lost notebook and unpublished papers. We prove the Mock Theta Conjectures with the help of Dyson’s rank and S. Ramanujan’s Mock Theta functions. These functions were quoted in Ramanujan’s lost notebook and unpublished papers. In1916, Ramanujan stated the theta series in x like A(x), B(x), C(x), D(x). We discuss the Ramanujan’s functions with the help of Dyson’s rank symbols. These functions are useful to prove the Mock Theta Conjectures. Now first Mock Theta Conjecture is “The number of partitions of 5n with rank congruent to 1 modulo 5 equals the number of partitions of 5n with rank congruent to 0 modulo 5 plus the number of partitions of n with unique smallest part and all other parts the double of the smallest part”, and Second Mock Theta Conjecture is “The double of the number of partitions of with rank congruent to 2 modulo 5 equals the sum of the number of partitions of with rank congruent to 0 and congruent to1 modulo 5, and the sum of one and the number of partitions of n with unique smallest part and all other parts  one plus the double of the smallest part”. This paper shows how to prove the Theorem 1.3 with the help of Dyson’s rank symbols N(0,5,5n+1), N(2,5, 5n+1) and shows how to prove the Theorem 1.4 with the help of Ramanujan’s theta series and Dyson’s rank symbols N(1,5, 5n+2), N(2,5, 5n+2) respectively.

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Folsom, Amanda. "Asymptotics and Ramanujan's mock theta functions: then and now." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 378, no. 2163 (December 9, 2019): 20180448. http://dx.doi.org/10.1098/rsta.2018.0448.

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This article is in commemoration of Ramanujan's election as Fellow of The Royal Society 100 years ago, as celebrated at the October 2018 scientific meeting at the Royal Society in London. Ramanujan's last letter to Hardy, written shortly after his election, surrounds his mock theta functions. While these functions have been of great importance and interest in the decades following Ramanujan's death in 1920, it was unclear how exactly they fit into the theory of modular forms—Dyson called this ‘a challenge for the future’ at another centenary conference in Illinois in 1987, honouring the 100th anniversary of Ramanujan's birth. In the early 2000s, Zwegers finally recognized that Ramanujan had discovered glimpses of special families of non-holomorphic modular forms, which we now know to be Bruinier and Funke's harmonic Maass forms from 2004, the holomorphic parts of which are called mock modular forms. As of a few years ago, a fundamental question from Ramanujan's last letter remained, on a certain asymptotic relationship between mock theta functions and ordinary modular forms. The author, with Ono and Rhoades, revisited Ramanujan's asymptotic claim, and established a connection between mock theta functions and quantum modular forms, which were not defined until 90 years later in 2010 by Zagier. Here, we bring together past and present, and study the relationships between mock modular forms and quantum modular forms, with Ramanujan's mock theta functions as motivation. In particular, we highlight recent work of Bringmann–Rolen, Choi–Lim–Rhoades and Griffin–Ono–Rolen in our discussion. This article is largely expository, but not exclusively: we also establish a new interpretation of Ramanujan's radial asymptotic limits in the subject of topology. This article is part of a discussion meeting issue ‘Srinivasa Ramanujan: in celebration of the centenary of his election as FRS’.

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Srivatsa, Kumar, K. R. Rajanna, and R. Narendra. "Theta function identities of level 6 and their application to partitions." Filomat 33, no. 11 (2019): 3323–35. http://dx.doi.org/10.2298/fil1911323s.

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M. Somos has conjectured many theta function identities belonging to different levels. He has done so with the use of a computer but has not chosen to validate these identities. We find that the mentioned identities are analogous to those discovered by Srinivasa Ramanujan. The intent to prove some of the identities prepared by Somos concerning theta function identities of a level six and to also establish certain partition-theoretic interpretations of these identities which we have been successfully proved here.

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Ono, Ken. "Srinivasa Ramanujan: in celebration of the centenary of his election as FRS." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 378, no. 2163 (December 9, 2019): 20190386. http://dx.doi.org/10.1098/rsta.2019.0386.

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Bietenholz, Wolfgang. "From Ramanujan to renormalization: the art of doing away with divergences and arriving at physical results." Revista Mexicana de Física E 18, no. 2 Jul-Dec (May 13, 2021): 020203. http://dx.doi.org/10.31349/revmexfise.18.020203.

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A century ago Srinivasa Ramanujan --- the great self-taught Indian genius of mathematics --- died, shortly after returning from Cambridge, UK, where he had collaborated with Godfrey Hardy. Ramanujan contributed numerous outstanding results to different branches of mathematics, like analysis and number theory, with a focus on special functions and series. Here we refer to apparently weird values which he assigned to two simple divergent series, $\sum_{n \geq 1} n$ and $\sum_{n \geq 1} n^{3}$. These values are sensible, however, as analytic continuations, which correspond to Riemann's $\zeta$-function. Moreover, they have applications in physics: we discuss the vacuum energy of the photon field, from which one can derive the Casimir force, which has been experimentally measured. We discuss its interpretation, which remains controversial. This is a simple way to illustrate the concept of renormalization, which is vital in quantum field theory.

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Qureshi, Mohammad Idris, and Mohd Shadab. "Uniﬁcation and Generalization of Two Product Theorems of Srinivasa Ramanujan Associated with Quadruple Hypergeometric Functions." Applied Mathematics & Information Sciences 11, no. 4 (July 1, 2017): 1225–34. http://dx.doi.org/10.18576/amis/110430.

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Arif, Bijoy Rahman. "An Inductive Proof of Bertrand's Postulate." GANIT: Journal of Bangladesh Mathematical Society 38 (January 14, 2019): 85–87. http://dx.doi.org/10.3329/ganit.v38i0.39788.

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In this paper, we are going to prove a famous problem concerning the prime numbers called Bertrand's postulate. It states that there is always at least one prime, p between n and 2n, means, there exists n < p < 2n where n > 1. It is not a newer theorem to be proven. It was first conjectured by Joseph Bertrand in 1845. He did not find a proof of this problem but made important numerical evidence for the large values of n. Eventually, it was successfully proven by Pafnuty Chebyshev in 1852. That is why it is also called Bertrand-Chebyshev theorem. Though it does not give very strong idea about the prime distribution like Prime Number Theorem (PNT) does, the beauty of Bertrand's postulate lies on its simple yet elegant definition. Historically, Bertrand's postulate is also very important. After Euclid's proof that there are infinite prime numbers, there was no significant development in the prime number distribution. Peter Dirichlet stated the standard form of Prime Number Theorem (PNT) in 1838 but it was merely a conjecture that time and beyond the scope of proof to the then mathematicians. Bertrand's postulate was a simply stated problem but powerful enough, easy to prove and could lead many more strong assumptions about the prime number distribution. Illustrious Indian mathematician, Srinivasa Ramanujan gave a shorter but elegant proof using the concept of Chebyshev functions of prime, υ(x), Ψ(x)and Gamma function, Γ(x) in 1919 which led to the concept of Ramanujan Prime. Later Paul Erdős published another proof using the concept of Primorial function, p# in 1932. The elegance of our proof lies on not using Gamma function yet finding the better approximations of Chebyshev functions of prime. The proof technique is very similar the way Ramanujan proved it but instead of using the Stirling's approximation to the binomial coefficients, we are proving similar results using well-known proving technique the mathematical induction and they lead to somewhat stronger than Ramanujan's approximation of Chebyshev functions of prime. GANIT J. Bangladesh Math. Soc.Vol. 38 (2018) 85-87

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Usiskin, Zalman. "The Development Into the Mathematically Talented." Journal of Secondary Gifted Education 11, no. 3 (February 2000): 152–62. http://dx.doi.org/10.4219/jsge-2000-623.

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From some schools come many students very talented in certain areas, while from others come none. These results, far beyond what any statistical variability would explain, suggest that talent is developed to a greater extent than is popularly believed. Here we identify seven distinct levels of talent in mathematics and describe the enormous effort needed to move from any level to the next higher. The magnitude of effort and guidance required helps explain why most people view their own ability to reach higher levels of mathematical talent as unrealistic. We also point out that Srinivasa Ramanujan, the extraordinarily intuitive Indian mathematician who is sometimes thought to be the prime example of a self-taught mathematician, did not learn in isolation, but had good schooling and had carefully studied a comprehensive advanced mathematical text. Consequently, we suggest that teachers interested in the gifted view themselves as developing students into being talented at least as much as developing students who are already talented.

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Singh, Honourable Justice Yatindra. "Srinivas Ramanujan – The Genius." Indian Journal of Science and Technology 5, no. 12 (December 20, 2012): 1–9. http://dx.doi.org/10.17485/ijst/2012/v5i12.21.

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TOSCANO, ANNA. "ROBERT KANIGEL, L'uomo che vide l'infinito. La vita breve di Srinivasa Ramanujan, genio della matematica, tr. it. di Maddalena Mendolicchio, Milano, Rizzoli, 2003, 462 pp. + ill., ISBN 88-17-87169-9, € 19,00." Nuncius 19, no. 2 (January 1, 2004): 788–91. http://dx.doi.org/10.1163/221058704x00632.

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Et al., Dr Capt K. Sujatha. "ADVANCED ICT TOOLS FOR IMPLEMENTATION OF THE COMPLEX CALCULATIVE STUDY." INFORMATION TECHNOLOGY IN INDUSTRY 9, no. 1 (March 18, 2021): 1388–95. http://dx.doi.org/10.17762/itii.v9i1.282.

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India being a nation of Mathematicians like Srinivasa Ramanujam, Aryabhata, Shakuntala Devi, and so forth is constantly celebrated for worldwide numerical commitments throughout time. In the current circumstance, math is a subject that most understudies attempt to dodge because of its extensive counts and complex definitions. Numerous nations around the globe have done several turns of events and developments for mathematical calculations in the field of Chemistry, Physics, Electronics, Computer Science, and so forth with the assistance of cutting-edge Information Communication Technology (ICT) apparatuses. Indian mathematical subsystems also need to evolve and upgrade to meet the global professional competition from the grassroots level. There is a genuine need to join ICT instruments for mathematics in school and college education to have a superior agreement. The joining of ICT instruments can change the course of calculative study to calculative upgrade which further prompts higher concept understanding and perspective development. This paper discusses the new improvement in the field of advanced calculation and how it is limiting the weight on understudies. As per Prytherch (2000), "ICTs are networks that provide new opportunities for teaching, learning, and training through the delivery of digital content. “Integration technology in education means giving experiential learning to the students. Software tools for calculation are utilized in the study hall for improving intellectual capacity and abilities in students especially to diminish computation stress among them.

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"Srinivasa Ramanujan." Physics Today, December 22, 2015. http://dx.doi.org/10.1063/pt.5.031117.

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"Srinivasa Ramanujan: a mathematical genius." Choice Reviews Online 36, no. 07 (March 1, 1999): 36–3959. http://dx.doi.org/10.5860/choice.36-3959.

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Ramachandra, K. "Little flowers to Srinivasa Ramanujan." Hardy-Ramanujan Journal Volume 32 (January 1, 2009). http://dx.doi.org/10.46298/hrj.2009.167.

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"Book reviews: India’s mathematical prodigy." Notes and Records of the Royal Society of London 48, no. 2 (July 31, 1994): 325–26. http://dx.doi.org/10.1098/rsnr.1994.0037.

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Robert Kanigel, The Man who Knew Infinity. A Life of the Genius Ramanujan . Abacus, 1991. Pp. 438. £6.99. ISBN 0-349-10452-2. This is the first fully researched biography of the most original person this century to come from the Indian sub-continent. In fact, this excellent book is almost two biographies for the price of one: the record of the life of Srinivasa Ramanujan is counterpointed with a more than adequate account of G.H. Hardy, the man who first fully proclaimed the mathematical genius of Ramanujan to the world. This biography relates in more detail the human side of Ramanujan’s life, which is only briefly covered in that classic vignette, Hardy’s obituary of him written for the Royal Society, 1 which should be read in conjunction with this book. 1. Proc. R. Soc. Lond . A 99, xiii-xxix (1921).

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Sivaraman, R. "Remembering Ramanujan." Advances in Mathematics: Scientific Journal, May 19, 2020, 489–506. http://dx.doi.org/10.37418/amsj.9.1.38.

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Mathematicians like Guido Grandi, Ernesto Cesaro and others found novel way of assigning finite sum to divergent series. This created a new scope of understanding leading to analytic continuation of real valued functions. One among such methods was called ``Ramanujan Summation'' proposed by Indian Mathematician Srinivasa Ramanujan. In this paper, I try to highlight how Ramanujan could have possibly arrived at those values by looking through his notebook jottings and extending further to provide Geometrical meaning behind those values obtained by him. Finally, I provide a novel way to arrive at the general formula obtained by Ramanujan regarding his summation of zeta function.

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Ramachandra, K. "Srinivasa Ramanujan (The inventor of the circle method) (22-12-1887 to 26-4-1920)." Hardy-Ramanujan Journal Volume 10 (January 1, 1987). http://dx.doi.org/10.46298/hrj.1987.102.

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International audience Ramanujan's first letter to Hardy states an asymptotic formula for the coefficient of $x^n$ in the expansion of $(\sum_{m=-\infty}^{\infty}(-1)^mx^{m^2})^{-1}$ which can be regarded as the genesis of the circle method. In this paper, we try to give some indication of the possible intuition of Ramanujan in his discovery of the circle method. We discuss briefly the Goldbach, Waring and partition problems. At the end of the paper, there is a brief discussion on Ramanujan's $\tau$ function

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"Srinivasa Ramanujan: The lost notebook and other unpublished papers." Choice Reviews Online 26, no. 10 (June 1, 1989): 26–5700. http://dx.doi.org/10.5860/choice.26-5700a.

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Agarwal, A. K., and G. Sood. "Split $(n+t)$-Color Partitions and Gordon-McIntosh Eight Order Mock Theta Functions." Electronic Journal of Combinatorics 21, no. 2 (June 9, 2014). http://dx.doi.org/10.37236/3726.

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In 2004, the first author gave the combinatorial interpretations of four mock theta functions of Srinivasa Ramanujan using $n$-color partitions which were introduced by himself and G.E. Andrews in 1987. In this paper we introduce a new class of partitions and call them "split $(n+t)$-color partitions". These new partitions generalize Agarwal-Andrews $(n+t)$-color partitions. We use these new combinatorial objects and give combinatorial meaning to two basic functions of Gordon-McIntosh found in 2000. They used these functions to establish the modular transformation formulas for certain eight order mock theta functions. The work done here has a great potential for future research.

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"Ramanujan’s illness." Notes and Records of the Royal Society of London 48, no. 1 (January 31, 1994): 107–19. http://dx.doi.org/10.1098/rsnr.1994.0009.

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A January night in 1913 found the two renowned Cambridge mathematicians G.H. Hardy and J.E. Littlewood, in the latter’s rooms in Trinity College, poring over an unsolicited manuscript of mathematical formulae, which had arrived that morning in Hardy’s mail. The letter was from a 25-year-old Hindu clerk, Srinivasa Ramanujan (1887-1920), who lived in Madras and was as regards mathematics entirely self-educated. Many mathematicians receive letters from cranks and hoaxers, but it was at once obvious that this author was no crank, since not one of his theorems, as E.H. Neville later pointed out, could have been set in even the most advanced mathematics examination in the world. The suspicion of a hoax by a competent mathematician, where familiar theorems are skilfully disguised, was dispelled by Hardy’s recognition that a few of the results defeated him completely; he had never seen anything the least like them before. ‘A single look at them is enough to show that they could only be written down by a mathematician of the highest class’. When they parted that night both Hardy and Littlewood were satisfied that their Indian correspondent was a mathematical genius, and within weeks Littlewood was comparing him with Jacobi, the great German master of formulae. This famous episode bore immediate fruit for Ramanujan. Hardy at once joined forces with others in Madras in obtaining a research studentship for him so that he could pursue mathematical research full-time, and in arranging his coming to Trinity College, Cambridge in April 1914 to work with Hardy and to have first-hand contact with European mathematicians.

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Abrar, Fildzah Nabilah, Anis Endang, and Harius Eko Saputra. "Representasi Orientalisme Dalam Film The Man Who Knew Infinity." Profesional: Jurnal Komunikasi dan Administrasi Publik 4, no. 2 (October 1, 2018). http://dx.doi.org/10.37676/professional.v4i2.624.

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Western unceasing production of the film with the character of the East that bad in it. To maintain the Orientalism of the West, adapt them to the times. Media of mass used is the mass media movie. Because of the film's West could easily represent Orientalism. The movie is popular and in demand, and can be watched by all ages. One Western movie that shows the representation of Orientalism is the movie The Man Who Knew Infinity. MovieThe Man Who Knew Infinity tells of the struggle of one of the Eastern scholars in the field of mathematics named Srinivasa Ramanujan. The movie represents the power and difference in social status between the West and the East. As well as how the Western view of the East or Orientalism.And to know the description or representation intentionally created by the movie, then the unambiguous approach to the Semiotic, to use Roland Barthes's model. So, this research want to find out how the meaning of denotation, connotation, and myth preformance of orientalism in the movie The Man Who Knew Infinity. Through the observation carefully and in collaboration with relevant documents, finally found the scene-the scene that can represent the orientalism in the film The Man Who Knew Infinity.The results showed that the representation of Orientalism that aredisplayed in the film this is a form of power of the West against the East. And the difference stastus social as well as position that are shown between the East and the West. Film director Matt Brown, accentuate how the West perceives the East. Although in the field of education of the East and the West have equality. But in class social status and position. The west and the East is not equal in the perspective of Orientalism.

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Yadav, Dr Dhiraj. "Srinivas Ramanujan: An Indigenous Mathematician." International Journal of Advanced Research in Science, Communication and Technology, March 16, 2021, 136–40. http://dx.doi.org/10.48175/ijarsct-848.

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The paper undertaken for the deliberation of International stature on December 22, 2020 rivets attention on the topic of THE CONTRIBUTION OF RAMANUJAN in the arena of MATHEMATICS. He is remembered for India’s greatest mathematical genii. He made significant contribution to the analytical theory of numbers elliptical functions, continued fractions and infinite series. Ramanujan left a slew of unpublished note books enfolding theorems that future generation of mathematical world have been exploring continuously. He is an icon of a self-studied, self learnt, self-taught mathematical genius who is a living legend and ennobling soul for the posterity. He is known as child prodigy. Owing to his ingenuous acumen and surprising accomplishments in the field of Mathematics, Indian govt. decided to celebrate his birthday 22nd December as National Mathematics Day.

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Alladi, Krishnaswami. "Touched by the Goddess." Inference: International Review of Science 2, no. 3 (September 28, 2016). http://dx.doi.org/10.37282/991819.16.32.

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A recent film starring Dev Patel and Jeremy Irons depicts Srinivasa Ramanujan’s fantastically original mathematical achievements and tragically early death at 32. Number theorist and expert on Ramanujan’s work Krishnaswami Alladi reviews The Man Who Knew Infinity.

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राजपूत, ेबांगना, and जितेन्द्र अवस्थी. "श्रीनिवास रामानुजन: एक सहज गणितज्ञ." SRI JNPG COLLEGE REVELATION A JOURNAL OF POPULAR SCIENCE 2, no. 01 (January 15, 2018). http://dx.doi.org/10.29320/sjnpgrj.v2i01.11041.

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Indian mathematician, Srinivas Ramanujan, lived a brief life. However, even in such a short period, he was successful in creating such ripples in the field of mathematics ,especially the research of the infinite series, that have made him immortal. This article throws light upon the extremely modest life this mathematical genius led and also on the beautiful mind we were privileged to have had among us.

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