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arXiv · 2304.09545

Certain Extensions of Results of Siegel, Wilton and Hardy

Pedro Ribeiro·Semyon Yakubovich
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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.

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Pedro Ribeiro, Semyon Yakubovich. 2023-04-19. Certain Extensions of Results of Siegel, Wilton and Hardy. https://arxiv.org/abs/2304.09545

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