# On the equivalence of Beukers-type and Sorokin-type multiple integrals

@article{Viola2012OnTE,
title={On the equivalence of Beukers-type and Sorokin-type multiple integrals},
author={Carlo Viola},
journal={Journal of Mathematical Sciences},
year={2012},
volume={180},
pages={561-568}
}
• C. Viola
• Published 2012
• Mathematics
• Journal of Mathematical Sciences
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 n-dimensional case of a similar equivalence between suitably defined Beukers-type and Sorokin-type multiple integrals, with consequences on the arithmetical structure of such integrals as linear combinations of zeta-values with rational coefficients.
2 Citations
Irrationality proofs for zeta values, moduli spaces and dinner parties
A simple geometric construction on the moduli spaces $\mathcal{M}_{0,n}$ of curves of genus $0$ with $n$ ordered marked points is described which gives a common framework for many irrationalityExpand

#### References

SHOWING 1-5 OF 5 REFERENCES
Multiple integrals and linear forms in zeta-values
• Mathematics
• 2007
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
Integral identities and constructions of approximations to zeta-values
Nous presentons une construction generale de combinaisons lineaires a coefficients rationnels en les valeurs de la fonction zeta de Riemann aux entiers. Ces formes lineaires sont exprimees en termesExpand
The group structure for ζ(3)
• Mathematics
• 2001
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
Séries hypergéométriques multiples et polyzêtas
• Mathematics
• 2006
Nous decrivons un algorithme theorique et effectif permettant de demontrer que des series et integrales hypergeometriques multiples relativement generales se decomposent en combinaisons lineaires aExpand
Groupes de Rhin-Viola et intégrales multiples
Ce texte donne une nouvelle presentation, et une generalisation, des groupes qui apparaissent dans les travaux de Rhin-Viola ([8], [9]) sur les mesures d'irrationalite de ζ(2) et ζ(3). D'une part, onExpand