The distribution of values of L(1,chi_d)

2002/06/04 by Andrew Granville, K. Soundararajan, Granville, Andrew +2
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.math/0206031

34 pages

arxiv created 2002/06/04 · openalex publication_date 2002/06/04 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we investigate the distribution of values of L(1,chi) as chi ranges over primitive real characters. In particular we focus on the extent to which this distribution may be approximated by "random Euler products." Our work also establishes a recent conjecture of Montgomery and Vaughan on the frequency of large (or small) values of L(1,chi).

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• Asymmetric Distribution of Extreme Values of Cubic L-functions at s=1
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• The Distribution of Values of (L')/(L)(1/2+ε,χ_D)