On the zeros of Dirichlet L-functions

Tatenda Isaac Kubalalika

Published 2020-06-16Version 1

Let $\chi$ be a Dirichlet character. Define $\Theta_\chi$ to be the supremum of the real parts of the zeros of the corresponding Dirichlet L-function $L(s, \chi)$. We demonstrate in this note that $\Theta_{\chi} < 1$ for all $\chi$. A particular corollary of our result would be an improved error bound for the Prime Number Theorem for arithmetic progressions.