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On multiple integrals represented as a linear form in 1, ζ(3), ζ(5),..., ζ(2k − 1)

Abstract

A theorem on the presentability of a multiple integral as a linear form in 1, ζ(3), ζ(5),..., ζ(2k − 1) over ℚ is proved. This theorem refines the results recently obtained by D. Vasiliev, V. Zudilin, and S. Zlobin.

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Correspondence to V. Salikhov.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 6, pp. 143–178, 2005.

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Salikhov, V., Frolovichev, A. On multiple integrals represented as a linear form in 1, ζ(3), ζ(5),..., ζ(2k − 1). J Math Sci 146, 5731–5758 (2007). https://doi.org/10.1007/s10958-007-0389-6

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Keywords

  • Linear Form
  • Zeta Function
  • Summing
  • Multiple Integral
  • Riemann Zeta Function