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Journal articles on the topic 'Riemann hypothesis'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Durmagambetov, Asset A. "Riemann Hypothesis." Journal of Applied Mathematics and Physics 05, no. 07 (2017): 1424–30. http://dx.doi.org/10.4236/jamp.2017.57117.

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2

Suman, Shekhar, and Raman Kumar Das. "A NOTE ON AN EQUIVALENT OF THE RIEMANN HYPOTHESIS." JOURNAL OF RAMANUJAN SOCIETY OF MATHEMATICS AND MATHEMATICAL SCIENCES 10, no. 01 (2022): 97–102. http://dx.doi.org/10.56827/jrsmms.2022.1001.8.

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In this manuscript we denote by P ρ a sum over the non trivial zeros of Riemann zeta function (or over the zeros of Riemann’s xi function), where the zeros of multiplicity k are counted k times. We prove a result that the Riemann Hypothesis is true if and only if

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3

Ravindran, Renuka. "The Riemann hypothesis." Resonance 11, no. 11 (2006): 40–47. http://dx.doi.org/10.1007/bf02834472.

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4

Whitley, Robert. "The Riemann Hypothesis, the Generalized Riemann Hypothesis, and the Cesáro Operator." Integral Equations and Operator Theory 61, no. 3 (2008): 433–48. http://dx.doi.org/10.1007/s00020-008-1594-5.

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5

Haight, David F. "Summa characteristicaand the Riemann hypothesis: scaling Riemann’s mountain." Journal of Interdisciplinary Mathematics 11, no. 6 (2008): 851–901. http://dx.doi.org/10.1080/09720502.2008.10700605.

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6

Galetto, Fausto. "Riemann’s Hypothesis New Proof." Applied Science and Innovative Research 6, no. 1 (2022): p14. http://dx.doi.org/10.22158/asir.v6n1p14.

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After some papers proving the RC (short for “Riemann’s Conjecture”, also known as the “Riemann’s Hypothesis”, RH), now the author provides a new proof, using the “Spira Criterion” that states “The RH is equivalent to the statement that if s>0.5 and t> 6.5 then |z(1-s)|> |z(s)|”. We use the concept of “transfer function” for control systems. This new proof is so simple that the author wonders why a great mathematician like Riemann did not see it; therefore F. Galetto thinks that somewhere in the purported proof there should be an error.

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7

Bayer, Pilar. "La hipòtesi de Riemann: El gran repte pendent." Mètode Revista de difusió de la investigació, no. 8 (June 5, 2018): 35. http://dx.doi.org/10.7203/metode.0.8903.

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The Riemann hypothesis is an unproven statement referring to the zeros of the Riemann zeta function. Bernhard Riemann calculated the first six non-trivial zeros of the function and observed that they were all on the same straight line. In a report published in 1859, Riemann stated that this might very well be a general fact. The Riemann hypothesis claims that all non-trivial zeros of the zeta function are on the the line x = 1/2. The more than ten billion zeroes calculated to date, all of them lying on the critical line, coincide with Riemann’s suspicion, but no one has yet been able to prove

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8

Deloin, R. "Proof of Riemann Hypothesis." Asian Research Journal of Mathematics 9, no. 1 (2018): 1–8. http://dx.doi.org/10.9734/arjom/2018/40341.

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9

Fei, Jinhua. "About the Riemann Hypothesis." Journal of Applied Mathematics and Physics 04, no. 03 (2016): 561–70. http://dx.doi.org/10.4236/jamp.2016.43061.

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10

Mazurkin, P. M. "Proof the Riemann Hypothesis." American Journal of Applied Mathematics and Statistics 2, no. 2 (2014): 53–59. http://dx.doi.org/10.12691/ajams-2-2-1.

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11

Sarnak, Peter. "The Grand Riemann Hypothesis." Milan Journal of Mathematics 78, no. 1 (2010): 61–63. http://dx.doi.org/10.1007/s00032-010-0126-3.

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12

Diaz-Vargas, Javier. "Riemann Hypothesis forFp[T]." Journal of Number Theory 59, no. 2 (1996): 313–18. http://dx.doi.org/10.1006/jnth.1996.0100.

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13

Frederick, Onwuka. "Riemann Hypothesis Original Proof." International Journal For Academic Research and Development 3, no. 1 (2021): 46–51. https://doi.org/10.5281/zenodo.6640652.

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14

PERELMAN, CARLOS CASTRO. "THE RIEMANN HYPOTHESIS IS A CONSEQUENCE OF $\mathcal{CT}$-INVARIANT QUANTUM MECHANICS." International Journal of Geometric Methods in Modern Physics 05, no. 01 (2008): 17–32. http://dx.doi.org/10.1142/s021988780800262x.

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The Riemann's hypothesis (RH) states that the nontrivial zeros of the Riemann zeta-function are of the form sn = 1/2 + iλn. By constructing a continuous family of scaling-like operators involving the Gauss–Jacobi theta series and by invoking a novel [Formula: see text]-invariant Quantum Mechanics, involving a judicious charge conjugation [Formula: see text] and time reversal [Formula: see text] operation, we show why the Riemann Hypothesis is true. An infinite family of theta series and their Mellin transform leads to the same conclusions.

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15

Bosco, Adriko. "Riemann Hypothesis and the Distribution of Prime Numbers." International Journal of Science and Research (IJSR) 10, no. 8 (2021): 538–47. https://doi.org/10.21275/mr21804185118.

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16

Pushkarev, Petr. "Constant quality of the Riemann zeta's non-trivial zeros." Global Journal of Pure and Applied Mathematics 13, no. 6 (2017): 1987–92. https://doi.org/10.5281/zenodo.822059.

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In this article we are closely examining Riemann zeta function's non-trivial zeros. Especially, we examine real part of non-trivial zeros. Real part of Riemann zeta function's non-trivial zeros is considered in the light of constant quality of such zeros. We propose and prove a theorem of this quality. We also uncover a definition phenomenons of zeta and Riemann xi functions. In conclusion and as an conclusion we observe Riemann hypothesis in perspective of our researches.

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17

Nakamura, Takashi. "A complete Riemann zeta distribution and the Riemann hypothesis." Bernoulli 21, no. 1 (2015): 604–17. http://dx.doi.org/10.3150/13-bej581.

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18

Sierra, Germán. "The Riemann Zeros as Spectrum and the Riemann Hypothesis." Symmetry 11, no. 4 (2019): 494. http://dx.doi.org/10.3390/sym11040494.

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We present a spectral realization of the Riemann zeros based on the propagation of a massless Dirac fermion in a region of Rindler spacetime and under the action of delta function potentials localized on the square free integers. The corresponding Hamiltonian admits a self-adjoint extension that is tuned to the phase of the zeta function, on the critical line, in order to obtain the Riemann zeros as bound states. The model suggests a proof of the Riemann hypothesis in the limit where the potentials vanish. Finally, we propose an interferometer that may yield an experimental observation of the

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19

Ghanouchi, Jamel. "A Proof of the Riemann Hypothesis." Bulletin of Mathematical Sciences and Applications 6 (November 2013): 1–5. http://dx.doi.org/10.18052/www.scipress.com/bmsa.6.1.

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In this paper, we present the Riemann problem and define the real primes. It allows to generalize the Riemann hypothesis to the reals. A calculus of integral solves the problem. We generalize the proof to the integers.

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20

Biswas, Jyotirmoy. "The proof of Riemann Hypothesis." IOSR Journal of Mathematics 7, no. 4 (2013): 14–20. http://dx.doi.org/10.9790/5728-0741420.

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21

Hutson, H. L. "Equidistribution and the Riemann hypothesis." Publicacions Matemàtiques 38 (January 1, 1994): 51–55. http://dx.doi.org/10.5565/publmat_38194_05.

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22

Planat, Michel, Patrick Solé, and Sami Omar. "Riemann hypothesis and quantum mechanics." Journal of Physics A: Mathematical and Theoretical 44, no. 14 (2011): 145203. http://dx.doi.org/10.1088/1751-8113/44/14/145203.

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23

Bonelli, A., and M. Rasetti. "Riemann hypothesis and dynamical systems." Le Journal de Physique IV 08, PR6 (1998): Pr6–189—Pr6–195. http://dx.doi.org/10.1051/jp4:1998625.

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24

Cobeli, Cristian, Marian Vâjâitu, and Alexandru Zaharescu. "Grahm's conjecture under riemann hypothesis." Journal of Number Theory 31, no. 1 (1989): 80–87. http://dx.doi.org/10.1016/0022-314x(89)90053-x.

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25

Chaitin, G. J. "Thoughts on the riemann hypothesis." Mathematical Intelligencer 26, no. 1 (2004): 4–7. http://dx.doi.org/10.1007/bf02985392.

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26

Mishou, Hidehiko, and Hirofumi Nagoshi. "Equivalents of the Riemann hypothesis." Archiv der Mathematik 86, no. 5 (2006): 419–24. http://dx.doi.org/10.1007/s00013-005-1375-1.

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27

Bump, Daniel, Kwok-Kwong Choi, Pär Kurlberg, and Jeffrey Vaaler. "A local Riemann hypothesis, I." Mathematische Zeitschrift 233, no. 1 (2000): 1–18. http://dx.doi.org/10.1007/pl00004786.

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28

Kurlberg, Pär. "A local Riemann hypothesis, II." Mathematische Zeitschrift 233, no. 1 (2000): 21–37. http://dx.doi.org/10.1007/pl00004791.

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29

He, Yang-Hui, Vishnu Jejjala, and Djordje Minic. "From Veneziano to Riemann: A string theory statement of the Riemann hypothesis." International Journal of Modern Physics A 31, no. 36 (2016): 1650201. http://dx.doi.org/10.1142/s0217751x16502018.

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We discuss a precise relation between the Veneziano amplitude of string theory, rewritten in terms of ratios of the Riemann zeta function, and two elementary criteria for the Riemann hypothesis formulated in terms of integrals of the logarithm and the argument of the zeta function. We also discuss how the integral criterion based on the argument of the Riemann zeta function relates to the Li criterion for the Riemann hypothesis. We provide a new generalization of this integral criterion. Finally, we comment on the physical interpretation of our recasting of the Riemann hypothesis in terms of t

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30

Basu, Pathikrit. "On Propositions Pertaining to the Riemann Hypothesis IV." Asian Journal of Probability and Statistics 27, no. 4 (2025): 68–76. https://doi.org/10.9734/ajpas/2025/v27i4740.

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In this paper, we enumerate certain hypotheses regarding the Riemann zeta function. The hypotheses are in the form of bounds on the norm of the tail of the sequence that determines the Riemann zeta function and also an optimization problem involving Diophantine approximation. These are related to Ω-phenomena, arising infinitely often along the imaginary axis, such as concentration phenomena. We also relate these hypotheses with the Riemann and Lindelof hypotheses.

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31

Wong, Bertrand. "Non-trivial zeros of riemann zeta function and riemann hypothesis." Bulletin of Pure & Applied Sciences- Mathematics and Statistics 41e, no. 1 (2022): 88–99. http://dx.doi.org/10.5958/2320-3226.2022.00013.3.

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32

Garunkštis, Ramūnas, and Antanas Laurinčikas. "The Riemann hypothesis and universality of the Riemann zeta-function." Mathematica Slovaca 68, no. 4 (2018): 741–48. http://dx.doi.org/10.1515/ms-2017-0141.

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Abstract We prove that, under the Riemann hypothesis, a wide class of analytic functions can be approximated by shifts ζ(s + iγk), k ∈ ℕ, of the Riemann zeta-function, where γk are imaginary parts of nontrivial zeros of ζ(s).

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33

Fayez, Fok Al Adeh. "How to prove the Riemann Hypothesis." Journal of Progressive Research in Mathematics 12, no. 2 (2017): 1853–66. https://doi.org/10.5281/zenodo.3975882.

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The aim of this paper is to prove the celebrated Riemann Hypothesis. I have already discovered a simple proof of the Riemann Hypothesis. The hypothesis states that the nontrivial zeros of the Riemann zeta function have real part equal to 0.5. I assume that any such zero is s = a+ bi. I use integral calculus in the first part of the proof. In the second part I employ variational calculus. Through equations (50) to (59) I consider (a) as a fixed exponent, and verify that a = 0.5 .From equation (60) onward I view (a) as a parameter (a <0.5 ) and arrive at a contradiction. At the end of the pro

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34

McPhedran, Ross C., Lindsay C. Botten, Dominic J. Williamson, and Nicolae-Alexandru P. Nicorovici. "The Riemann hypothesis and the zero distribution of angular lattice sums." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 467, no. 2133 (2011): 2462–78. http://dx.doi.org/10.1098/rspa.2010.0566.

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We give analytical results pertaining to the distributions of zeros of a class of sums which involve complex powers of the distance to points in a two-dimensional square lattice and trigonometric functions of their angle. Let denote the product of the Riemann zeta function and the Catalan beta function, and let denote a particular set of angular sums. We then introduce a function that is the quotient of the angular lattice sums with , and use its properties to prove that obeys the Riemann hypothesis for any m if and only if obeys the Riemann hypothesis. We furthermore prove that if the Riemann

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35

Shivakumar M D. "The Riemann hypothesis and its implications." World Journal of Advanced Research and Reviews 10, no. 3 (2021): 493–98. https://doi.org/10.30574/wjarr.2021.10.3.0287.

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The Riemann Hypothesis, one of the most significant unsolved problems in mathematics, posits that all non-trivial zeros of the Riemann zeta function have a real part equal to 1/2. This paper examines the formulation of the hypothesis, its historical context, attempts at proof, and its profound implications across various mathematical domains. We explore connections to prime number distribution, quantum mechanics, and cryptography, highlighting why the hypothesis remains central to modern mathematics. While a proof remains elusive, understanding the hypothesis and its consequences provides cruc

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36

Durmagambetov, A. A. "The Riemann Hypothesis-Millennium Prize Problem." Advances in Pure Mathematics 06, no. 12 (2016): 915–20. http://dx.doi.org/10.4236/apm.2016.612069.

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37

Wu, Hefa. "The Riemann Hypothesis Is not Equality." International Journal of Applied Physics and Mathematics 7, no. 2 (2017): 134–40. http://dx.doi.org/10.17706/ijapm.2017.7.2.134-140.

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38

Kanemitsu, S., and M. Yoshimoto. "Farey series and the Riemann hypothesis." Acta Arithmetica 75, no. 4 (1996): 351–74. http://dx.doi.org/10.4064/aa-75-4-351-374.

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39

Wójtowicz, Marek. "Robin's inequality and the Riemann hypothesis." Proceedings of the Japan Academy, Series A, Mathematical Sciences 83, no. 4 (2007): 47–49. http://dx.doi.org/10.3792/pjaa.83.47.

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40

Fei, Jinhua. "Riemann Hypothesis and Value Distribution Theory." Journal of Applied Mathematics and Physics 05, no. 03 (2017): 734–40. http://dx.doi.org/10.4236/jamp.2017.53062.

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41

Verjovsky, Alberto. "Discrete measures and the Riemann hypothesis." Kodai Mathematical Journal 17, no. 3 (1994): 596–608. http://dx.doi.org/10.2996/kmj/1138040054.

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42

Bettin, Sandro, and Steven M. Gonek. "THE CONJECTURE IMPLIES THE RIEMANN HYPOTHESIS." Mathematika 63, no. 1 (2016): 29–33. http://dx.doi.org/10.1112/s0025579316000139.

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43

Schumayer, Dániel, and David A. W. Hutchinson. "Colloquium: Physics of the Riemann hypothesis." Reviews of Modern Physics 83, no. 2 (2011): 307–30. http://dx.doi.org/10.1103/revmodphys.83.307.

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44

de Reyna, Juan Arias. "A Test for the Riemann Hypothesis." Functiones et Approximatio Commentarii Mathematici 38, no. 2 (2008): 159–70. http://dx.doi.org/10.7169/facm/1229696537.

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45

Hwan Yun, Young. "A Proof of the Riemann Hypothesis." American Journal of Applied Mathematics and Statistics 12, no. 4 (2024): 86–92. https://doi.org/10.12691/ajams-12-4-3.

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46

Doju K. Degefa. "Quantum Hidden Variables and Riemann Hypothesis." Multimedia Research 7, no. 4 (2024): 15–27. http://dx.doi.org/10.46253/j.mr.v7i4.a2.

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47

Cox, Darrell, and Pedro Caceres. "The Riemann Hypothesis and Polar Coordinates." Global Journal of Pure and Applied Mathematics 20, no. 3 (2024): 439–62. http://dx.doi.org/10.37622/gjpam/20.3.2024.439-462.

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48

Chahal, Jasbir S., and Brian Osserman. "The Riemann Hypothesis for Elliptic Curves." American Mathematical Monthly 115, no. 5 (2008): 431–42. http://dx.doi.org/10.1080/00029890.2008.11920545.

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49

Akbary, Amir, and Zachary Friggstad. "Superabundant Numbers and the Riemann Hypothesis." American Mathematical Monthly 116, no. 3 (2009): 273–75. http://dx.doi.org/10.1080/00029890.2009.11920937.

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50

Lachaud, Gilles. "Spectral analysis and the Riemann hypothesis." Journal of Computational and Applied Mathematics 160, no. 1-2 (2003): 175–90. http://dx.doi.org/10.1016/s0377-0427(03)00621-6.

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