Calendar

Posted August 22, 2026

Algebra and Number Theory Seminar Questions or comments?

Aniketh Sivakumar, Tulane University
TBA

Event contact: Gene Kopp

Posted August 22, 2026
Last modified September 9, 2026

Algebra and Number Theory Seminar Questions or comments?

Paresh Singh Arora, LSU
Reductions of Certain Well-Poised Hypergeometric Character Sums

Whipple’s classical reduction formulas express well-poised hypergeometric series either as products and quotients of gamma values or as gamma factors multiplied by hypergeometric functions, typically of smaller length. Building on work by Greene, McCarthy, and Li–Long–Tu, we establish finite field analogues of three very well-poised identities corresponding to $_4F_3(-1)$, $_5F_4(1)$, and $_6F_5(-1)$. We show that the associated $\ell$-adic Galois representations constructed by Katz and Beukers–Cohen–Mellit are reducible, explicitly identifying one of their constituents in a way that reflects the corresponding Whipple decompositions. As an application, we obtain new correspondences between well-poised hypergeometric data and modular forms.

Event contact: Gene Kopp

Posted August 22, 2026

Algebra and Number Theory Seminar Questions or comments?

Isabella Negrini, University of Toronto
TBA

Event contact: Gene Kopp