نتایج جستجو برای: the riemann function

تعداد نتایج: 16183382  

Journal: :J. London Math. Society 2014
David W. Farmer Steven M. Gonek Yoonbok Lee

Abstract. The complex zeros of the Riemannn zeta-function are identical to the zeros of the Riemann xi-function, ξ(s). Thus, if the Riemann Hypothesis is true for the zetafunction, it is true for ξ(s). Since ξ(s) is entire, the zeros of ξ(s), its derivative, would then also satisfy a Riemann Hypothesis. We investigate the pair correlation function of the zeros of ξ(s) under the assumption that ...

Journal: :Journal of Number Theory 1987

2001
Dmitry Korotkin

In these notes we solve a class of Riemann-Hilbert (inverse monodromy) problems with an arbitrary quasi-permutation monodromy group. The solution is given in terms of Szegö kernel on the underlying Riemann surface. In particular, our construction provides a new class of solutions of the Schlesinger system. We present some results on explicit calculation of the corresponding tau-function, and de...

2004
Xavier Gourdon

In this paper, we present an optimization of Odlyzko and Schönhage algorithm that computes efficiently Zeta function at large height on the critical line, together with computation of zeros of the Riemann Zeta function thanks to an implementation of this technique. The first family of computations consists in the verification of the Riemann Hypothesis on all the first 10 non trivial zeros. The ...

Journal: :Nagoya Mathematical Journal 1959

Journal: :Bulletin of the American Mathematical Society 1999

Journal: :Journal of Inequalities and Applications 2018

2004
H. Gopalkrishna Gadiyar

In this brief note we bring out the analogy between the arithmetic of elliptic curves and the Riemann zeta-function. · · · The aim of this note is to point out the possibility of developing the theory of elliptic curves so that the arithmetical and analytic aspects are developed in strict analogy with the classical theory of the Riemann zeta-function. This has been triggered by Lemmermeyer’s pe...

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