# Twelfth moment of Dirichlet L-functions to prime power moduli

## TL;DR

This paper establishes a new result on the twelfth moment of Dirichlet L-functions for prime power moduli, extending previous work on the Riemann zeta function to a broader class of L-functions.

## Contribution

It proves the q-aspect analogue of Heath-Brown's twelfth moment result for Dirichlet L-functions with prime power moduli, using p-adic stationary phase methods.

## Key findings

- Established the q-aspect twelfth moment bound for Dirichlet L-functions
- Extended Heath-Brown's results to prime power moduli
- Complemented existing bounds for smooth square-free moduli

## Abstract

We prove the q-aspect analogue of Heath-Brown's result on the twelfth power moment of the Riemann zeta function for Dirichlet L-functions to odd prime power moduli. Our results rely on the p-adic method of stationary phase for sums of products and complement Nunes' bound for smooth square-free moduli.