The Riemann Hypothesis for Dirichlet $L$ Functions

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 $\zeta (s)$- a particular case of the Generalized Riemann Hypothesis.

10 pages, 3 figures

References in corpus (2)

• The Riemann Hypothesis for Symmetrised Combinations of Zeta Functions
• The Riemann Hypothesis for Angular Lattice Sums

Cited by in corpus (2)

• Some experiments in number theory
• Constructing a Proof of the Riemann Hypothesis