The second moment of cubic Dirichlet L-functions over function fields

2025/05/17 by Shivani Goel, Anwesh Ray, Goel, Shivani +1 · 1 citation
Mathematics · #11M38 #11R58 #11R59 #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Meromorphic and Entire Functions #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2505.12015

openalex publication_date 2025/05/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we study the second moment of cubic Dirichlet L-functions at the central point s=1/2 over the rational function field \mathbbF_q(T), where q is a power of an odd prime satisfying q ≡ 2 \pmod3. Our result extends prior work of David, Florea and Lalin, who obtained an asymptotic formula for the first moment. Our approach relies on analytic techniques (Perron's formula, approximate functional equation, etc), adapted to the function field context. A key step in the construction is to relate second moment to certain averages of Gauss sums, which are estimated in loc. cit. using results of Kubota and Hoffstein.

Citations

• Non-vanishing for cubic Hecke L-functions
• The fourth moment of quadratic Dirichlet L--functions over function\n fields

Cited by

• Twisted second moment of primitive cubic L-functions

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