Effective Brauer-Siegel theorems for Artin L-functions

2025/10/02 by Peter J. Cho, Cho, Peter J., Robert J. Lemke Oliver +3
Mathematics · #Analytic Number Theory Research #Advanced Algebra and Geometry #Finite Group Theory Research

paper · pdf · doi:10.48550/arxiv.2510.02309

Abstract

Given a number field K ≠ ℚ, in a now classic work, Stark pinpointed the possible source of a so-called Landau-Siegel zero of the Dedekind zeta function ζ_K(s) and used this to give effective upper and lower bounds on the residue of ζ_K(s) at s=1. We extend Stark's work to give effective upper and lower bounds for the leading term of the Laurent expansion of general Artin L-functions at s=1 that are, up to the value of implied constants, as strong as could reasonably be expected given current progress toward the generalized Riemann hypothesis. Our bounds are completely unconditional, and rely on no unproven hypotheses about Artin L-functions.

Citations

• Asymmetric Distribution of Extreme Values of Cubic L-functions at s=1

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