An Explicit Result for $|L(1+it,\chi)|$

TL;DR

This paper provides an explicit upper bound for non-principal Dirichlet L-functions on the line s=1+it, which helps improve the accuracy of zero-counting formulas for these functions.

Contribution

It introduces a new explicit upper bound for non-principal Dirichlet L-functions on the line s=1+it, enhancing zero distribution analysis.

Findings

Derived an explicit upper bound for |L(1+it,χ)|

Improved error estimates in zero-counting formulas

Applicable to non-principal Dirichlet L-functions

Abstract

We give an explicit upper bound for non-principal Dirichlet $L$-functions on the line $s=1+it$. This result can be applied to improve the error in the zero-counting formulae for these functions.