4F3-Gaussian hypergeometric series and traces of Frobenius for elliptic curves.

In this article, we obtain finite field analogues of classical summation identities connecting F 3 -Appell series and 4 F 3 -classical hypergeometric series. As an application, we establish a new summation formula satisfied by the 4 F 3 -Gaussian hypergeometric series. We further express certain special values of 4 F 3 -Gaussian hypergeometric series in terms of traces of the Frobenius endomorphisms of certain families of elliptic curves. We also explicitly find some special values of 4 F 3 -Gaussian hypergeometric series. [ABSTRACT FROM AUTHOR]