Distribution of the Hessian values of Gaussian hypergeometric functions

2024/05/25 by Ken Ono, Sudhir Pujahari, Ono, Ken +5
Mathematics · #FOS: Mathematics #Mathematical functions and polynomials #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2405.16349

openalex publication_date 2024/05/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a special family of Gaussian hypergeometric functions whose entries are cubic and trivial characters over finite fields. The special values of these functions are known to give the Frobenius traces of families of Hessian elliptic curves. Using the theory of harmonic Maass forms and mock modular forms, we prove that the limiting distribution of these values is semi-circular (i.e. SU(2)), confirming the usual Sato-Tate distribution in this setting.

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