An improved upper bound for the error in the zero-counting formulae for Dirichlet $L$-functions and Dedekind zeta-functions

TL;DR

This paper provides new explicit upper bounds on the number of zeros of Dirichlet L-functions and Dedekind zeta-functions within specified rectangles, improving our understanding of their zero distributions.

Contribution

It introduces an improved upper bound for zero-counting formulas for Dirichlet L-functions and Dedekind zeta-functions, enhancing previous estimates.

Findings

New explicit upper bounds for zero counts

Improved estimates for zero distribution in rectangles

Enhanced understanding of L-function zeroes

Abstract

This paper contains new explicit upper bounds for the number of zeroes of Dirichlet L-functions and Dedekind zeta-functions in rectangles.