Certain Extensions of Results of Siegel, Wilton and Hardy
Number Theory
2023-05-09 v2 Classical Analysis and ODEs
Abstract
Recently, Dixit et al. established a very elegant generalization of Hardy's Theorem concerning the infinitude of zeros that the Riemann zeta function possesses at its critical line. By introducing a general transformation formula for the theta function involving the Bessel and Modified Bessel functions of the first kind, we extend their result to a class of Dirichlet series satisfying Hecke's functional equation. In the process, we also find new generalizations of classical identities in Analytic number theory.
Keywords
Cite
@article{arxiv.2304.09545,
title = {Certain Extensions of Results of Siegel, Wilton and Hardy},
author = {Pedro Ribeiro and Semyon Yakubovich},
journal= {arXiv preprint arXiv:2304.09545},
year = {2023}
}
Comments
More details are given in Subsection 3.1 regarding the method used in the proof of Theorem 1.1; We added Lemma 3.1 which clarifies an assertion made on page 36 of the previous version; Minor typos in the text corrected