The Experts below are selected from a list of 11472 Experts worldwide ranked by ideXlab platform
V E Korepin - One of the best experts on this subject based on the ideXlab platform.
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quantum spin chains and Riemann Zeta Function with odd arguments
Journal of Physics A, 2001Co-Authors: Hermann Boos, V E KorepinAbstract:The Riemann Zeta Function is an important object of number theory. We argue that it is related to the Heisenberg spin-1/2 anti-ferromagnet. In the XXX spin chain we study the probability of formation of a ferromagnetic string in the anti-ferromagnetic ground state in the thermodynamics limit. We prove that for short strings the probability can be expressed in terms of the Riemann Zeta Function with odd arguments.
Warren Tai - One of the best experts on this subject based on the ideXlab platform.
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Is the Riemann Zeta Function in a short interval a 1-RSB spin glass ?
Sojourns in Probability Theory and Statistical Physics - I, 2019Co-Authors: Louis-pierre Arguin, Warren TaiAbstract:Fyodorov, Hiary & Keating established an intriguing connection between the maxima of log-correlated processes and the ones of the Riemann Zeta Function on a short interval of the critical line. In particular, they suggest that the analogue of the free energy of the Riemann Zeta Function is identical to the one of the Random Energy Model in spin glasses. In this paper, the connection between spin glasses and the Riemann Zeta Function is explored further. We study a random model of the Riemann Zeta Function and show that its two-overlap distribution corresponds to the one of a one-step replica symmetry breaking (1-RSB) spin glass. This provides evidence that the local maxima of the Zeta Function are strongly clustered.
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is the Riemann Zeta Function in a short interval a 1 rsb spin glass
arXiv: Probability, 2019Co-Authors: Louis-pierre Arguin, Warren TaiAbstract:Fyodorov, Hiary & Keating established an intriguing connection between the maxima of log-correlated processes and the ones of the Riemann Zeta Function on a short interval of the critical line. In particular, they suggest that the analogue of the free energy of the Riemann Zeta Function is identical to the one of the Random Energy Model in spin glasses. In this paper, the connection between spin glasses and the Riemann Zeta Function is explored further. We study a random model of the Riemann Zeta Function and show that its two-overlap distribution corresponds to the one of a one-step replica symmetry breaking (1-RSB) spin glass. This provides evidence that the local maxima of the Zeta Function are strongly clustered.
Chaoping Chen - One of the best experts on this subject based on the ideXlab platform.
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certain relationships among polygamma Functions Riemann Zeta Function and generalized Zeta Function
Journal of Inequalities and Applications, 2013Co-Authors: Junesang Choi, Chaoping ChenAbstract:Many useful and interesting properties, identities, and relations for the Riemann Zeta Function ζ (s) and the Hurwitz Zeta Function ζ (s, a) have been developed. Here, we aim at giving certain (presumably) new and (potentially) useful relationships among polygamma Functions, Riemann Zeta Function, and generalized Zeta Function by modifying Chen's method. We also present a double inequality approximating ζ (2r + 1) by a more rapidly convergent series. MSC: Primary 11M06; 33B15; secondary 40A05; 26D07
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Certain relationships among polygamma Functions, Riemann Zeta Function and generalized Zeta Function
Journal of Inequalities and Applications, 2013Co-Authors: Junesang Choi, Chaoping ChenAbstract:Many useful and interesting properties, identities, and relations for the Riemann Zeta Function ζ ( s ) Open image in new window and the Hurwitz Zeta Function ζ ( s , a ) Open image in new window have been developed. Here, we aim at giving certain (presumably) new and (potentially) useful relationships among polygamma Functions, Riemann Zeta Function, and generalized Zeta Function by modifying Chen’s method. We also present a double inequality approximating ζ ( 2 r + 1 ) Open image in new window by a more rapidly convergent series.
Shaoji Feng - One of the best experts on this subject based on the ideXlab platform.
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on gaps between zeros of the Riemann Zeta Function
Journal of Number Theory, 2012Co-Authors: Shaoji FengAbstract:Abstract Assuming the Riemann Hypothesis, we show that infinitely often consecutive non-trivial zeros of the Riemann Zeta-Function differ by at least 2.7327 times the average spacing and infinitely often they differ by at most 0.5154 times the average spacing.
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Zeros of the Riemann Zeta Function on the critical line
Journal of Number Theory, 2012Co-Authors: Shaoji FengAbstract:Abstract We introduce a new mollifier and apply the method of Levinson and Conrey to prove that at least 41.28 % of the zeros of the Riemann Zeta Function are on the critical line. The method may also be used to improve other results on zeros relate to the Riemann Zeta Function, as well as conditional results on prime gaps.
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Zeros of the Riemann Zeta Function on the critical line
arXiv: Number Theory, 2010Co-Authors: Shaoji FengAbstract:it is proved that at least 41.28% zeros of the Riemann Zeta Function are on the critical line
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Difference independence of the Riemann Zeta Function
Acta Arithmetica, 2006Co-Authors: Yik-man Chiang, Shaoji FengAbstract:It is proved that the Riemann Zeta Function does not satisfy any nontrivial algebraic difference equation whose coefficients are meromorphic Functions $\phi$ with Nevanlinna characteristic satisfying $T(r, \phi)=o(r)$ as $r\to \infty$
Hermann Boos - One of the best experts on this subject based on the ideXlab platform.
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quantum spin chains and Riemann Zeta Function with odd arguments
Journal of Physics A, 2001Co-Authors: Hermann Boos, V E KorepinAbstract:The Riemann Zeta Function is an important object of number theory. We argue that it is related to the Heisenberg spin-1/2 anti-ferromagnet. In the XXX spin chain we study the probability of formation of a ferromagnetic string in the anti-ferromagnetic ground state in the thermodynamics limit. We prove that for short strings the probability can be expressed in terms of the Riemann Zeta Function with odd arguments.
