Abstract
Using properties of certain character sums over finite fields, we here obtain some transformations for finite field Appell series F2â and F4â in terms of F34-Gaussian hypergeometric series. These motivate us to find a finite field analog for certain transformations satisfied by the classical Appell series F2 and F4. We also deduce an expression for the finite field Appell series F4â in terms of F23-Gaussian hypergeometric series. Consequently, we investigate connections of trace of Frobenius endomorphism for certain families of elliptic curves and the finite field Appell series F4â.
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