Hyperkloosterman sums revisited

We return to some past studies of hyperkloosterman sums ([9,10]) via p-adic cohomology with an aim to improve earlier results. In particular, we work here with Dwork's θ_∞-splitting function and a better choice of basis for cohomology. To a large extent, we are guided to this choice of basis by our recent work on the p-integrality of coefficients of A-hypergeometric series [3]. In the earlier work, congruence estimates were limited to p>n+2. We are here able to remove all characteristic restrictions from earlier results.