The number of -points on Dwork hypersurfaces and hypergeometric functions

We provide a formula for the number of F p -points on the Dwork hypersurface x 1 n + x 2 n ⋯ + x n n - n λ x 1 x 2 … x n = 0 in terms of a p -adic hypergeometric function previously defined by the author. This formula holds in the general case, i.e., for any n , λ ∈ F p ∗ and for all odd primes p , thus extending results of Goodson and Barman et al. which hold in certain special cases.