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We extend our previous work on hypergeometric point count formulas by provingthat we can express the number of points on families of Dwork hypersurfaces$$X_{\lambda}^d: \hspace{.1in} x_1^d+x_2^d+\ldots+x_d^d=d\lambda x_1x_2\cdotsx_d$$ over finite fields of order $q\equiv 1\pmod d$ in terms of Greene'sfinite field hypergeometric functions. We prove that when $d$ is odd, thenumber of points can be expressed as a sum of hypergeometric functions plus$(q^{d-1}-1)/(q-1)$ and conjecture that this is also true when $d$ is even. Theproof rests on a result that equates certain Gauss sum expressions with finitefield hypergeometric functions. Furthermore, we discuss the types ofhypergeometric terms that appear in the point count formula and give anexplicit formula for Dwork threefolds.

A Complete Hypergeometric Point Count Formula for Dwork Hypersurfaces