数学大讲堂

Hypergeometric functions over finite fields

Abstract: Hypergeometric functions are special functions with lot of symmetries.  In this talk, we will introduce hypergeometric functions over finite fields, originally due to Greene, Katz and McCarthy, in a way that is parallel to the classical hypergeometric functions, and discuss their properties and applications to character sums and the arithmetic of hypergeometric abelian varieties. This is a joint work with Jenny Fuselier, Ravi Ramakrishna, Holly Swisher, and Fang-Ting Tu.


Most of the talk will be accessible to senior undergraduate students.