An explicit hybrid estimate for $L(1/2+it,\chi)$

TL;DR

This paper derives an explicit hybrid estimate for Dirichlet L-functions at the critical line, providing a Weyl bound especially effective when the modulus is a sixth power, with applications of van der Corput--Weyl type lemmas.

Contribution

It introduces a new explicit hybrid estimate for $L(1/2+it,\, ext{ extbackslash chi})$, including simplified forms for sixth power moduli and new hybrid lemmas.

Findings

Derived an explicit Weyl bound for $L(1/2+it,\, ext{ extbackslash chi})$

Provided simplified estimates when $q$ is a sixth power

Presented several hybrid lemmas of van der Corput--Weyl type

Abstract

An explicit hybrid estimate for $L(1/2+it,\chi)$ is derived, where $\chi$ is a Dirichlet character modulo $q$. The estimate applies when $t$ is bounded away from zero, and is most effective when $q$ is powerfull, yielding an explicit Weyl bound in this case. The estimate takes a particularly simple form if $q$ is a sixth power. Several hybrid lemmas of van der Corput--Weyl type are presented.