Using Dwork's theory, the authors prove a broad generalization of his famous p-adic formal congruences theorem. This enables them to prove certain p-adic congruences for the generalized hypergeometric series with rational parameters in particular, they hold for any prime number p and not only for almost all primes. Furthermore, using Christol's functions, the authors provide an explicit formula for the ``Eisenstein constant'' of any hypergeometric series with rational parameters. As an application of these results, the authors obtain an arithmetic statement ``on average'' of a new type...
Using Dwork's theory, the authors prove a broad generalization of his famous p-adic formal congruences theorem. This enables them to prove certain p-a...
