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

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 for… Expand

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 our… Expand

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 the… Expand

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-type… Expand