Hypergeometric functions over ${\mathbb{F}}_q$ and traces of Frobenius for elliptic curves

Abstract

We present here explicit relations between the traces of Frobenius endomorphisms of certain families of elliptic curves and special values of ${}_2{F}_1$-hypergeometric functions over ${\mathbb{F}}_q$ for $q\equiv 1(\text{mod}6)$ and $q\equiv 1(\text{mod}4)$.

8 pages, Proc. Amer. Math. Soc., accepted for publication