Conjectures and experiments concerning the moments of L(1/2,χ_d)

2011/10/03 by Matthew W. Alderson, Michael Rubinstein, Alderson, Matthew W. +2 · 1 citation
Computer Science · Mathematics · Social Sciences · #11M06 #Analytic Number Theory Research #Coding theory and cryptography #FOS: Mathematics #Historical Geopolitical and Social Dynamics #Limits and Structures in Graph Theory #Number Theory (math.NT) #math.NT #msc:11M06

paper · pdf · doi:10.48550/arxiv.1110.0253

openalex publication_date 2011/10/03 · arxiv created 2012/03/01 · arxiv updated 2012/03/02 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

We report on some extensive computations and experiments concerning the moments of quadratic Dirichlet L-functions at the critical point. We computed the values of L(1/2,χ_d) for - 5× 10¹⁰ < d < 1.3 × 10¹⁰ in order to numerically test conjectures concerning the moments ∑_|d|<X L(1/2,χ_d)^k. Specifically, we tested the full asymptotics for the moments conjectured by Conrey, Farmer, Keating, Rubinstein, and Snaith, as well as the conjectures of Diaconu, Goldfeld, Hoffstein, and Zhang concerning additional lower terms in the moments. We also describe the algorithms used for this large scale computation.

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