Secondary terms in the asymptotics of moments of L-functions

2020/08/30 by Adrian Diaconu, Diaconu, Adrian, Henry Twiss +1
Computer Science · Mathematics · Social Sciences · #Analytic Number Theory Research #Coding theory and cryptography #FOS: Mathematics #Historical Geopolitical and Social Dynamics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2008.13297

openalex publication_date 2020/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We propose a refined version of the existing conjectural asymptotic formula for the moments of the family of quadratic Dirichlet L-functions over rational function fields. Our prediction is motivated by two natural conjectures that provide sufficient information to determine the analytic properties (meromorphic continuation, location of poles, and the residue at each pole) of a certain generating function of moments of quadratic L-functions. The number field analogue of our asymptotic formula can be obtained by a similar procedure, the only difference being the contributions coming from the archimedean and even places, which require a separate analysis. To avoid this additional technical issue, we present, for simplicity, the asymptotic formula only in the rational function field setting. This has also the advantage of being much easier to test.

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