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. 
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References

SHOWING 1-5 OF 5 REFERENCES
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
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)
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
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