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Mathematische Annalen

, Volume 347, Issue 4, pp 739–763 | Cite as

A refinement of Nesterenko’s linear independence criterion with applications to zeta values

  • Stéphane Fischler
  • Wadim Zudilin
Open Access
Article

Abstract

We refine (and give a new proof of) Nesterenko’s famous linear independence criterion from 1985, by making use of the fact that some coefficients of linear forms may have large common divisors. This is a typical situation appearing in the context of hypergeometric constructions of \({\mathbb{Q}}\)-linear forms involving zeta values or their q-analogs. We apply our criterion to sharpen previously known results in this direction.

Keywords

Linear Form Rational Approximation Acta Arith Positive Divisor Viola Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2009

Authors and Affiliations

  1. 1.Laboratoire de Mathématiques d’OrsayUniversité Paris-SudOrsay CedexFrance
  2. 2.CNRSOrsay CedexFrance
  3. 3.School of Mathematical and Physical SciencesUniversity of NewcastleCallaghanAustralia

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