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

2025/08/05 by Palojärvi, Neea, Zhao, Tianyu · 1 citation
#11L07 #11M41 #11Y35 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2508.03023

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.

Citations

• Conditional estimates for L-functions in the Selberg class II
• Explicit estimates for Artin L-functions: Duke's short-sum theorem and\n Dedekind Zeta Residues
• On the explicit upper and lower bounds for the number of zeros of the Selberg class
• Improvements to Turing’s method
• Some Calculations of the Riemann Zeta-Function

Cited by

• Upper bounds on gaps between zeros of L-functions
• Explicit conditional bounds for the residue of a Dedekind zeta-function at s=1

Related

• Large values of L-functions from the Selberg class
• A method for proving the completeness of a list of zeros of certain L-functions
• On the explicit upper and lower bounds for the number of zeros of the Selberg class
• Unconditional estimates on the argument of Dirichlet L-functions with applications to low-lying zeros
• Effective Brauer-Siegel theorems for Artin L-functions