PIMS Distinguished Visitor Seminar: Frits Beukers

By the end of the 1980's several authors introduced the concept of hypergeometric function on a finite field. Although this is a purely number theoretical finite sum, it shares many properties with its analytic counterpart. The special values of these functions turn out to be related to point counting on algebraic varieties over finite fields or better, traces of Frobenius operators. In this lecture we introduce these finite hypergeometric functions and describe some of their properties.