Dear all,
The next talk is by Sudhir Kumar Pujahari of the National Institute of Science Education and Research (NISER), Bhubaneswar, India.
Talk Announcement:
Title: Moments of the Trace of Frobenius in Arithmetic Progressions.
Title: Moments of the Trace of Frobenius in Arithmetic Progressions.
Speaker: Sudhir Kumar Pujahari, NISER (Bhubaneshwar, India)
When: Feb 12, 2026, 4:00 PM- 5:00 PM IST
When: Feb 12, 2026, 4:00 PM- 5:00 PM IST
Where: Zoom: Write to the organisers for the link.
Abstract
The statistical distribution of the trace of Frobenius for elliptic curves is a central theme in arithmetic geometry, famously encapsulated by the Sato–Tate conjecture. In this talk, we investigate the moments of the trace of Frobenius for elliptic curves over finite fields when the traces are constrained to a fixed arithmetic progression. We establish the asymptotic behavior of the moment as the size of the finite field tends to infinity. In the process, we will see a bridge between moments of traces of Frobenius and the theory of binary quadratic forms; specifically, we will derive these results from new asymptotic formulas for sums of Hurwitz class numbers restricted to arithmetic progressions. This talk is based on joint work with Ben Kane and Kathrin Bringmann.
Gaurav Bhatnagar, Atul Dixit, and Krishnan Rajkumar,
Special Functions and Number Theory Seminar
