Asymmetric Distribution of Extreme Values of Cubic L-functions at s=1

2023/06/23 by Pranendu Darbar, Chantal David, Darbar, Pranendu +5 · 1 citation
Mathematics · Social Sciences · #11M06 #11M20 #11R16 #Analytic Number Theory Research #FOS: Mathematics #Historical Geopolitical and Social Dynamics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2306.13626

openalex publication_date 2023/06/23 · openalex created_date 2023/06/27 · openalex updated_date 2026/07/28

Abstract

We investigate the distribution of values of cubic Dirichlet L-functions at s=1. Following ideas of Granville and Soundararajan for quadratic L-functions, we model the distribution of L(1,χ) by the distribution of random Euler products L(1,\mathbbX) for certain family of random variables \mathbbX(p) attached to each prime. We obtain a description of the proportion of |L(1,χ)| that are larger or that are smaller than a given bound, and yield more light into the Littlewood bounds. Unlike the quadratic case, there is an asymmetry between lower and upper bounds for the cubic case, and small values are less probable than large values.

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