The eighth moment of Dirichlet L-functions II

TL;DR

This paper establishes an asymptotic formula for the eighth moment of Dirichlet L-functions averaged over primitive characters, moduli, and a short segment on the critical line, extending previous conditional results.

Contribution

It provides an unconditional proof of the eighth moment asymptotic formula, removing the reliance on the Generalized Riemann Hypothesis.

Findings

Unconditional asymptotic formula for the eighth moment of Dirichlet L-functions.

Extension of previous conditional results to unconditional ones.

Advancement in understanding moments of L-functions in analytic number theory.

Abstract

We prove an asymptotic formula for the eighth moment of Dirichlet $L$-functions averaged over primitive characters $\chi$ modulo $q$, over all moduli $q\leq Q$ and with a short average on the critical line. Previously the same result was shown conditionally on the Generalized Riemann Hypothesis by the first two authors.