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The group structure for ζ(3)
1. Introduction. In his proof of the irrationality of ζ(3), Apéry [1] gave sequences of rational approximations to ζ(2) = π 2 /6 and to ζ(3) yielding the irrationality measures µ(ζ(2)) < 11.85078. ..Expand
Generalized Vandermonde determinants
This paper is organized as follows: In this chapter we give a general background. In chapter 2 we give some important definitions to be used in the following. In chapter 3 we prove an expression forExpand
The permutation group method for the dilogarithm
We give qualitative and quantitative improvements on all the best pre- viously known irrationality results for dilogarithms of positive rational numbers. We obtain such improvements by applying ourExpand
On the equivalence of Beukers-type and Sorokin-type multiple integrals
It is well known that a triple Beukers-type integral, as defined by G. Rhin and C. Viola, can be transformed into a suitable triple Sorokin-type integral. I will discuss possible extensions to theExpand
Multiple integrals and linear forms in zeta-values
We deflne n-dimensional Beukers-type integrals over the unit hypercube. Using an n-dimensional birational transformation we show that such integrals are equal to suita- ble n-dimensional Sorokin-typeExpand