Explicit Upper Bounds for $|L(1, \chi)|$ when $\chi(3)=0$

TL;DR

This paper derives explicit upper bounds for the absolute value of L-series at 1 for primitive Dirichlet characters with conductors divisible by 3, contributing to the understanding of L-series behavior in number theory.

Contribution

It provides the first explicit upper bounds for |L(1, χ)| specifically when the conductor q is divisible by 3, filling a gap in existing bounds.

Findings

Established explicit bounds for |L(1, χ)| when 3 divides q

Enhanced understanding of L-series behavior at s=1

Applicable to primitive Dirichlet characters with conductor divisible by 3

Abstract

Let $\chi$ be a primitive Dirichlet character of conductor $q$ and $L(z,\chi)$ the associated L-series. In this paper we provide an explicit upper bound for $|L(1, \chi)|$ when 3 divides $q$.