On Turing's method for Artin $L$-functions and the Selberg class

TL;DR

This paper derives explicit bounds for classes of L-functions, enhancing Turing's method for zero counting, with implications for understanding zeros of Artin L-functions and the Selberg class.

Contribution

It provides new explicit bounds for L-functions, generalizing previous estimates and enabling more effective zero detection methods.

Findings

Derived explicit bounds for classes of L-functions

Improved estimates for zero counting using Turing's method

Applicable to Artin L-functions and the Selberg class

Abstract

We derive explicit bounds for two general classes of $L$-functions, improving and generalizing earlier known estimates. These bounds can be used, for example, to apply Turing's method for determining the number of zeros up to a given height.