Results 11 to 20 of about 640,811 (318)
On primeness of the Selberg zeta-function [PDF]
arXiv, 2019 In this note we prove that the Selberg zeta-function associated to a compact Riemann surface is pseudo-prime and right-prime in the sense of a decomposition.
Ramūnas Garunkštis, Jörn Steuding
arxiv +4 more sources
A pseudo zeta function and the distribution of primes [PDF]
Proceedings of the National Academy of Sciences, 2000 The Riemann zeta function is given by: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{equation*}{\zeta}(s)={ \,\substack{ ^{{\infty}} \\ {\sum}
Paul R. Chernoff
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The prime number theorem and pair correlation of zeros of the Riemann zeta-function [PDF]
Research in Number Theory, 2022 We prove that the error in the prime number theorem can be quantitatively improved beyond the Riemann Hypothesis bound by using versions of Montgomery’s conjecture for the pair correlation of zeros of the Riemann zeta-function which are uniform in long ...
D. Goldston, Ade Irma Suriajaya
semanticscholar +3 more sources
Zeta function zeros, powers of primes, and quantum chaos [PDF]
Physical Review E, 2003 We present a numerical study of Riemann's formula for the oscillating part of the density of the primes and their powers. The formula is comprised of an infinite series of oscillatory terms, one for each zero of the zeta function on the critical line and was derived by Riemann in his paper on primes assuming the Riemann hypothesis.
Jamal Sakhr +2 more
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On primeness of the Selberg zeta-function [PDF]
Hokkaido Mathematical Journal, 2020 Comment: To appear in Hokkaido Mathematical ...
Ramūnas Garunkštis, Jörn Steuding
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Selberg zeta-function associated to compact Riemann surface is prime [PDF]
Revista de la Unión Matemática Argentina, 2021 Let Z(s) be the Selberg zeta-function associated to a compact Riemann surface. We consider decompositions Z(s) = f(h(s)), where f and h are meromorphic functions, and show that such decompositions can only be trivial.
Ramūnas Garunkštis
openalex +4 more sources
The Ihara zeta function as a partition function for network structure characterisation [PDF]
Scientific ReportsStatistical characterizations of complex network structures can be obtained from both the Ihara Zeta function (in terms of prime cycle frequencies) and the partition function from statistical mechanics.
Jianjia Wang, Edwin R. Hancock
doaj +2 more sources
Orbit Growth of Periodic-Finite-Type Shifts via Artin–Mazur Zeta Function
Mathematics, 2020 The prime orbit and Mertens’ orbit counting functions describe the growth of closed orbits in a discrete dynamical system in a certain way. In this paper, we prove the asymptotic behavior of these functions for a periodic-finite-type shift.
Azmeer Nordin, Mohd Salmi Md Noorani
doaj +2 more sources
Beurling Zeta Functions, Generalised Primes, and Fractal Membranes [PDF]
Acta Applicandae Mathematicae, 2004 We study generalised prime systems $\mathcal{P ...
Titus Hilberdink, Michel L. Lapidus
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The pair correlation of zeros of the Riemann zeta function and distribution of primes [PDF]
Archiv der Mathematik, 2001 Assuming a special version of the Montgomery-Odlyzko law on the pair correlation of zeros of the Riemann zeta function conjectured by Rudnick and Sarnak and assuming the Riemann Hypothesis, we prove new results on the prime number theorem, difference of consecutive primes, and the twin prime conjecture.
Jingwen Liu, Y. Ye
openalex +2 more sources