Relevant bibliographies by topics / Srinivasa Ramanujan

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Academic literature on the topic 'Srinivasa Ramanujan'

Author: Grafiati
Published: 4 June 2021
Last updated: 5 February 2022

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Journal articles on the topic "Srinivasa Ramanujan"

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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Dissertations / Theses on the topic "Srinivasa Ramanujan"

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Souza, Matheus Bernardini de. "A equação de Ramanujan-Nagell e algumas de suas generalizações." reponame:Repositório Institucional da UnB, 2013. http://repositorio.unb.br/handle/10482/13573.

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Dissertação (mestrado)—Universidade de Brasília, Departamento de Matemática, 2013.
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O objetivo deste trabalho é mostrar algumas técnicas para resolução de equações diofantinas. Métodos algébricos são ferramentas de grande utilidade para a resolução da equação equation x2 + 7 = yn, em que y = 2 ou Y é ímpar. O uso do método hipergeométrico traz um resultado recente (de 2008) no estudo da equação x2 + 7 =2n. m e técnicas algébricas garantem uma condição necessária para que essa última equação tenha solução. _______________________________________________________________________________________ ABSTRACT
The objective of this work is to show some techniques for solving Diophantine equations. Algebraic methods are useful tools for solving the equation x2 + 7 = yn, where y = 2 or y is odd. The use of the hypergeometric method brings a recent result (from 2008) in the study of the equation x2 + 7 = 2n.m and algebraic techniques ensure a necessary condition for the last equation to have a solution.
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Lam, Heung Yeung. "q-series in number theory and combinatorics : a thesis presented in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Mathematics at Massey University, Albany, New Zealand." 2006. http://hdl.handle.net/10179/1477.

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Srinivasa Ramanujan (1887-1920) was one of the world's greatest mathematical geniuses. He work extensively in a branch of mathematics called "q-series". Around 1913, he found an important formula which now is known as Ramanujan's 1ψ1summation formula. The aim of this thesis is to investigate Ramanujan's 1ψ1summation formula and explore its applications to number theory and combinatorics. First, we consider several classical important results on elliptic functions and then give new proofs of these results using Ramanujan's 1ψ1 summation formula. For example, we will present a number of classical and new solutions for the problem of representing an integer as sums of squares (one of the most celebrated in number theory and combinatorics) in this thesis. This will be done by using q-series and Ramanujan's 1ψ1 summation formula. This in turn will give an insight into how Ramanujan may have proven many of his results, since his own proofs are often unknown, thereby increasing and deepening our understanding of Ramanujan's work.
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Books on the topic "Srinivasa Ramanujan"

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Rajagopalan, K. R. Srinivasa Ramanujan. Madras: Sri Aravinda-Bharati, 1988.

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Srinivas, K. Srinivasa Ramanujan. Bengaluru: Prism Books Pvt. Ltd., 2012.

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Srinivasa Rao, K. Srinivasa Ramanujan. Singapore: Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-16-0447-8.

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Srinivasa Ramanujan: A mathematical genius. Chennai: East West Books, 1998.

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K, Srinivasa Rao. Srinivasa Ramanujan: A mathematical genius. Chennai: East West Books (Madras), 2004.

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Aiyangar, Srinivasa Ramanujan. Collected papers of Srinivasa Ramanujan. Providence, RI: AMS Chelsea Pub., 2000.

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Murty, M. Ram, and V. Kumar Murty. The Mathematical Legacy of Srinivasa Ramanujan. India: Springer India, 2013. http://dx.doi.org/10.1007/978-81-322-0770-2.

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Kumar, Murty V., and SpringerLink (Online service), eds. The Mathematical Legacy of Srinivasa Ramanujan. India: Springer India, 2013.

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9

Srinivasa Ramanujan : The Lost Notebook and other Unpublished Papers. New York: Springer-Verlag, 1988.

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10

Abdi, W. H. Toils and triumphs of Srinivasa Ramanujan, the man and the mathematician. Jaipur: National, 1992.

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Book chapters on the topic "Srinivasa Ramanujan"

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Rao, K. Srinivasa. "Life of Srinivasa Ramanujan." In Srinivasa Ramanujan, 1–53. Singapore: Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-16-0447-8_1.

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Rao, K. Srinivasa. "Ramanujan Birth Anniversaries and Documentaries on Ramanujan." In Srinivasa Ramanujan, 203–18. Singapore: Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-16-0447-8_8.

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Rao, K. Srinivasa. "Chandrasekhar (Chandra) and Ramanujan." In Srinivasa Ramanujan, 161–82. Singapore: Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-16-0447-8_6.

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Rao, K. Srinivasa. "Books on Ramanujan and Busts of Ramanujan." In Srinivasa Ramanujan, 183–202. Singapore: Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-16-0447-8_7.

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Rao, K. Srinivasa. "Relevance of Ramanujan Today." In Srinivasa Ramanujan, 219–30. Singapore: Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-16-0447-8_9.

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Rao, K. Srinivasa. "Hardy on Ramanujan." In Srinivasa Ramanujan, 127–41. Singapore: Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-16-0447-8_4.

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Rao, K. Srinivasa. "Ramanujan at Cambridge." In Srinivasa Ramanujan, 55–82. Singapore: Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-16-0447-8_2.

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Rao, K. Srinivasa. "Ramanujan and Hypergeometric Series." In Srinivasa Ramanujan, 143–60. Singapore: Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-16-0447-8_5.

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Rao, K. Srinivasa. "Ramanujan’s Mathematics: Further Glimpses." In Srinivasa Ramanujan, 83–126. Singapore: Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-16-0447-8_3.

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E. H. Neville. "Srinivasa Ramanujan [redacted]." In Ramanujan: Essays and Surveys, 107–12. Providence, Rhode Island: American Mathematical Society, 2001. http://dx.doi.org/10.1090/hmath/022/16.

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