The Normal Distribution as a Limit of Generalized Sato-Tate Measures

2008/10/11 by Michael Larsen, Larsen, Michael
Mathematics · #11T23 #22E46 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.0810.2012

openalex publication_date 2008/10/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

With suitable order of limits, as p, m, and n all tend to infinity, the distribution of the normalized trace of Frobenius on H¹ of a "random" plane curve of degree n over the field with p^m elements, tends to a Gaussian distribution. The same is true of a "random" curve of genus g over the field with p^m elements.

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