The fourth moment of quadratic Dirichlet $L$-Functions II
Number Theory
2024-02-05 v1
Abstract
We prove an asymptotic formula with four main terms for the fourth moment of quadratic Dirichlet -functions unconditionally. Our proof is based on the work of Li , Soundararajan, and Soundararajan-Young. Our proof requires several new ingredients. These include a modified large sieve estimate for quadratic characters where we consider a fourth moment, rather than a second, as well as observing cross cancellations between diagonal and off-diagonal terms, which involves somewhat delicate combinatorial arguments.
Keywords
Cite
@article{arxiv.2402.01497,
title = {The fourth moment of quadratic Dirichlet $L$-Functions II},
author = {Quanli Shen and Joshua Stucky},
journal= {arXiv preprint arXiv:2402.01497},
year = {2024}
}