The Riemann Hypothesis for Dirichlet L Functions

2013/08/29 by McPhedran, Ross C.
#FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1308.6431

Abstract

This paper studies the connections between the zeros and their distribution functions for two particular Dirichlet L functions: the Riemann zeta function, and the Catalan beta function, also known as the Dirichlet beta function. It is shown that the Riemann hypothesis holds for the Dirichlet beta function L_-4(s) if and only if it holds for ζ(s)- a particular case of the Generalized Riemann Hypothesis.

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