The fourth moment of quadratic Dirichlet \(L\)-Functions II

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 f...

Full description

Saved in:
Bibliographic Details
Published inarXiv.org
Main Authors Shen, Quanli, Stucky, Joshua
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 02.02.2024
Subjects
Combinatorial analysis
Dirichlet problem
Online AccessGet full text

Cover

More Information
Summary: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.
ISSN:2331-8422