On the third moment of L((1)/(2), χ_d) I: the rational function field case

2018/01/01 by Adrian Diaconu, Diaconu, Adrian
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.1801.00486

openalex publication_date 2018/01/01 · openalex created_date 2022/09/10 · openalex updated_date 2026/07/28

Abstract

In this note, we prove the existence of a secondary term in the asymptotic formula of the cubic moment of quadratic Dirichlet L-functions ∑_\substackd - monic & sq. free deg d = D L(\tfrac12, χ_d)³ over rational function fields on the order of q^{\scriptscriptstyle (3)/(4) D}. This term is in perfect analogy with the x^{\scriptscriptstyle (3)/(4)}-term indicated in our joint work arXiv:math/0110092v1 for the corresponding asymptotic formula over the rationals.

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