Texas A&M Number Theory Seminar

Jenny Fuselier

Abstract: In the 1980s, Greene and Stanton introduced the notion of hypergeometric functions over a finite field.  They showed that these functions satisfy many properties and relations similar to those enjoyed by classical hypergeometric functions.  In this talk, we will introduce hypergeometric functions over F_p and then explore the relationships their values have to counting points on elliptic curves over F_p.  In particular, we will prove a theorem giving an explicit relationship between the values of a certain hypergeometric function over F_p and the number of points on the family of elliptic curves with j-invariant 1728/t.