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Proves Rivoal's 'denominator conjecture' concerning the common denominators of coefficients of certain linear forms in zeta values; these forms were constructed to obtain lower bounds for the dimension of the vector space over $mathbb Q$ spanned by $1,zeta

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...