Functiones et Approximatio Commentarii Mathematici

Multiple integrals and linear forms in zeta-values

Georges Rhin and Carlo Viola

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Abstract

We define $n$-dimensional Beukers-type integrals over the unit hypercube. Using an $n$-dimensional birational transformation we show that such integrals are equal to suitable $n$-dimensional Sorokin-type integrals with linear constraints, and represent linear forms in $1, \zeta(2), \zeta(3), \dots, \zeta(n)$ with rational coefficients.

Article information

Source
Funct. Approx. Comment. Math., Volume 37, Number 2 (2007), 429-444.

Dates
First available in Project Euclid: 18 December 2008

Permanent link to this document
https://projecteuclid.org/euclid.facm/1229619663

Digital Object Identifier
doi:10.7169/facm/1229619663

Mathematical Reviews number (MathSciNet)
MR2363836

Zentralblatt MATH identifier
1193.11073

Subjects
Primary: 11J72: Irrationality; linear independence over a field
Secondary: 11M06: $\zeta (s)$ and $L(s, \chi)$

Keywords
multiple integrals of rational functions values of the Riemann zeta-function birational transformations

Citation

Rhin, Georges; Viola, Carlo. Multiple integrals and linear forms in zeta-values. Funct. Approx. Comment. Math. 37 (2007), no. 2, 429--444. doi:10.7169/facm/1229619663. https://projecteuclid.org/euclid.facm/1229619663


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