The fourth moment of quadratic Dirichlet L-Functions II

2024/02/02 by Quanli Shen, Shen, Quanli, Joshua Stucky +1 · 1 citation
Mathematics · #11M06 #11M50 #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Meromorphic and Entire Functions #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2402.01497

openalex publication_date 2024/02/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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• Explicit quadratic large sieve inequality

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