Distribution of the Hessian values of Gaussian hypergeometric functions
Number Theory
2025-02-14 v3
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. ), confirming the usual Sato-Tate distribution in this setting.
Keywords
Cite
@article{arxiv.2405.16349,
title = {Distribution of the Hessian values of Gaussian hypergeometric functions},
author = {Ken Ono and Sudhir Pujahari and Hasan Saad and Neelam Saikia},
journal= {arXiv preprint arXiv:2405.16349},
year = {2025}
}
Comments
Addresses minor typos