Uniform approximation of some Dirichlet series by partial products of Euler type
General Mathematics
2013-08-06 v4 Number Theory
Abstract
In the present work we show that the Dirichlet series with the Euler product having analytical continuation to the critical strip without singularities, in some natural conditions, can be approximated by partial products of Euler type in the critical strip, if the primes over which are taken the products are distributed by a suitable way. The family of such series includes many of widely used Dirichlet series as the zeta-function, Dirichlet L-functions and etc. As a consequence the analog of the Riemann Hypothesis for such series is proven.
Cite
@article{arxiv.1008.0852,
title = {Uniform approximation of some Dirichlet series by partial products of Euler type},
author = {Ilgar Shikar Jabbarov},
journal= {arXiv preprint arXiv:1008.0852},
year = {2013}
}
Comments
The method of the paper based on a new measure introduced in infinite dimensional unit cube