Explicit estimates for Artin $L$-functions: Duke's short-sum theorem and Dedekind Zeta Residues

TL;DR

This paper proves explicit bounds for Artin L-functions and Dedekind zeta residues under GRH, extending Duke's short-sum theorem with precise numerical constants.

Contribution

It provides the first explicit version of Duke's short-sum theorem for Artin L-functions and applies it to obtain bounds on Dedekind zeta residues.

Findings

Explicit bounds for Artin L-functions under GRH

Bounds for Dedekind zeta residues derived from L-function estimates

All constants in the bounds are explicitly computed

Abstract

Under GRH, we establish a version of Duke's short-sum theorem for entire Artin $L$-functions. This yields corresponding bounds for residues of Dedekind zeta functions. All numerical constants in this work are explicit.