The fourth moment of quadratic Dirichlet $L$-Functions II

Quanli Shen, Joshua Stucky

Type: Preprint

Publication Date: 2024-02-02

Citations: 0

DOI: https://doi.org/10.48550/arxiv.2402.01497

Abstract

We prove an asymptotic formula with four main terms for the fourth moment of quadratic Dirichlet $L$-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.

Locations

arXiv (Cornell University) - View - PDF

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