La fonction hypergeometrique. Le groupe hypergeometrique. La forme hermitienne invariante. Le cas imprimitif. Theorie de Galois differentielle. Fonctions hypergeometriques algebriques

At the “Journees Arithmetiques” held at Marseille-Luminy in June 1978, R. Apery confronted his audience with a miraculous proof for the irrationality of ζ(3) = l-3+ 2-3+ 3-3 + .... The proof was… Expand

Abstract In 1979 R. Apery introduced the numbers a n = Σ 0 n ( k n ) 2 ( k n + k ) 2 in his irrationality proof for ζ(3). We prove some congruences for these numbers, which extend congruences… Expand

Abstract In 1979 R. Apery introduced the numbers an = Σ0n(kn)2(kn + k) and un = Σ0n(kn)2(kn + k)2 in his irrationality proof for ζ(2) and ζ(3). We prove some congruences for these numbers which… Expand

We give a basic introduction to the properties of Gauss’ hypergeometric functions, with an emphasis on the determination of the monodromy group of the Gaussian hypergeometric equation.

Finite hypergeometric functions are complex valued functions on finite fields which are the analogue of the classical analytic hypergeometric functions. From the work of N.M.Katz it follows that… Expand

has not more than 3× 7d+2s solutions. Since s ≥ d/2 this implies that (2) has at most 3× 74s solutions. We can apply this result to equation (1). However, the estimate will depend on the degree of… Expand