Seminar at SMU Delhi
April 25, 2018 (Wednesday) ,
3:30 PM at Webinar
Certain Character sums, hypergeometric series, and their connections to algebraic curves
Abstract of Talk
In this talk, we discuss certain transformations for the $p$-adic hypergeometric series which can be described as $p$-adic analogues of hypergeometric series. In particular, we discuss a Kummer's linear transformation and a transformation of Clausen. To derive these transformations we consider certain character sums involving quadratic characters. These transformations lead to many special values of $p$-adic hypergeometric series as well as finite field hypergeometric functions introduced by Greene. Also, we talk about their connections to algebraic curves.