Explicit upper bound for $\left|L(1, \chi)\right|$ when $\chi(2)=1$ and $\chi$ is even

TL;DR

This paper derives an explicit upper bound for the value of the Dirichlet L-series at 1 for primitive even characters with specific properties, aiding in understanding their size and behavior.

Contribution

The paper introduces a new explicit upper bound for |L(1, χ)| for primitive even Dirichlet characters with χ(2)=1, filling a gap in existing bounds.

Findings

Established a concrete upper bound for |L(1, χ)|

Applicable to primitive even characters with χ(2)=1

Enhances understanding of L-series behavior at 1

Abstract

Let $\chi$ be a primitive Dirichlet character of conductor $q$ and let us denote by $L(z, \chi)$ the associated $L$-series. In this paper, we provide an explicit upper bound for $\left|L(1, \chi)\right|$ when $\chi$ is a primitive even Dirichlet character with $\chi(2)=1$.