Results 11 to 20 of about 3,702 (270)
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
openalex +4 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
openalex +6 more sources
On primeness of the Selberg zeta-function [PDF]
Hokkaido Mathematical Journal, 2020 Comment: To appear in Hokkaido Mathematical ...
Ramūnas Garunkštis, Jörn Steuding
openalex +5 more sources
Prime zeta function statistics and Riemann zero-difference repulsion [PDF]
Journal of Statistical Mechanics: Theory and Experiment, 2021 Fixed more typos and minor ...
Gordon Chavez, Altan Allawala
openalex +4 more sources
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
A note on prime zeta function and Riemann zeta function. Corrigendum [PDF]
Notes on Number Theory and Discrete Mathematics, 2021 In [1] the author proposed two new results concerning the prime zeta function and the Riemann zeta function but they turn out to be wrong. In the present paper we provide their correct form.
Mladen Vassilev-Missana
openalex +2 more sources
Prime number theory and the Riemann zeta-function [PDF]
, 2005 D. R. Heath‐Brown
openalex +4 more sources
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
Prime pairs and the zeta function
Journal of Approximation Theory, 2008 AbstractAre there infinitely many prime pairs with given even difference? Most mathematicians think so. Using a strong arithmetic hypothesis, Goldston, Pintz and Yildirim have recently shown that there are infinitely many pairs of primes differing by at most sixteen.There is extensive numerical support for the prime-pair conjecture (PPC) of Hardy and ...
Jacob Korevaar
openalex +4 more sources
Arithmetic forms of Selberg zeta functions with applications to prime geodesic theorem [PDF]
Proceedings of the Japan Academy, Series A, Mathematical Sciences, 2002 We obtain an arithmetic expression of the Selberg zeta function for cocompact Fuchsian group defined via an indefinite division quaternion algebra over $\mathbf{Q}$. As application to the prime geodesic theorem, we prove certain uniformity of the distribution.
Tsuneo Arakawa +2 more
openalex +4 more sources