### Algebra SeminarDistribution Of Values Of Gaussian Hypergeometric FunctionsKen Ono (University Of Virginia)

Wednesday, December 1, 2021
11:15am – 12:05pm

Storrs Campus
Zoom

In the 1980's, Greene defined hypergeometric functions over finite fields using Jacobi sums. The framework of his theory establishes that these functions possess many properties that are analogous to those of the classical hypergeometric series studied by Gauss and Kummer. These functions have played important roles in the study of Apéry-style supercongruences, the Eichler-Selberg trace formula, Galois representations, and zeta-functions of arithmetic varieties. We study the value distribution (over large finite fields) of natural families of these functions, which turn out to encode the arithmetical statistical properties of families of elliptic curves and K3 surfaces. We use these results to obtain Sato-Tate type distributions. For the $$2F1$$ functions, the limiting distribution is semicircular (i.e. $$SU(2)$$), whereas the distribution for the $$3F2$$ functions is the Batman distribution for the traces of the real orthogonal group $$O_3$$. This is joint work with Hasan Saad and Neelam Saikia.

Contact the organizer for the Zoom link.

Contact:

mihai.fulger@uconn.edu

Algebra Seminar (primary), College of Liberal Arts and Sciences, UConn Master Calendar