## Thursday, September 16, 2021

### Neelam Saikia (University of Virginia), Thursday, September, 16, 2021 - 3:55 PM (IST)

Dear all,

The next talk is by Neelam Saikia who is currently a post-doc with Ken Ono at the University of Virginia.

Talk Announcement:

Title: Frobenius trace distributions for Gaussian hypergeometric functions

Speaker: Neelam Saikia (University of Virginia)

When: Thursday, September 16, 2021 - 4:00 PM - 5:00 PM (IST)

Where: Zoom: Please write to sfandnt@gmail.com for a link.

Live Link: https://youtu.be/o7qNW8BhgJI

Tea or Coffee: Please bring your own.

Abstract:

In the 1980's, Greene defined hypergeometric functions over finite fields using Jacobi sums. These functions possess many properties that are analogous to those of the classical hypergeometric series studied by Gauss, Kummer and others. These functions have played important roles in the study of supercongruences, the Eichler-Selberg trace formula, and zeta-functions of arithmetic varieties. We study the distribution (over large finite fields) of the values of certain families of these functions. For the $_2F_1$ functions, the limiting distribution is semicircular, whereas the distribution for the $_3F_2$ functions is the more exotic \it{Batman distribution.}

Gaurav Bhatnagar (Ashoka), Atul Dixit (IIT, Gandhinagar) and Krishnan Rajkumar (JNU)

sfandnt@gmail.com

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