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.
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The work of W. Zudilin was supported by the Max Planck Institute for Mathematics (Bonn) and the Hausdorff Center for Mathematics (Bonn).
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Fischler, S., Zudilin, W. A refinement of Nesterenko’s linear independence criterion with applications to zeta values. Math. Ann. 347, 739–763 (2010). https://doi.org/10.1007/s00208-009-0457-y
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DOI: https://doi.org/10.1007/s00208-009-0457-y