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Monodromy for the hypergeometric functionnFn−1
La fonction hypergeometrique. Le groupe hypergeometrique. La forme hermitienne invariante. Le cas imprimitif. Theorie de Galois differentielle. Fonctions hypergeometriques algebriques
A Note on the Irrationality of ζ(2) and ζ(3)
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 wasExpand
Another congruence for the Apéry numbers
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 congruencesExpand
Some Congruences for the Apery Numbers
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 whichExpand
Gauss’ Hypergeometric Function
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
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 thatExpand
The equation x+y=1 in finitely generated groups
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 ofExpand