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

Stephan Ramon Garcia; Ethan Simpson Lee

paper

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

arXiv:2101.11853

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.

arXiv comment20 pages, to appear in the Journal of Number Theorey

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

Abstract

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