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Properties of coefficients of certain linear forms in generalized polylogarithms. (English. Russian original) Zbl 1204.11111
J. Math. Sci., New York 146, No. 2, 5655-5668 (2007); translation from Fundam. Prikl. Mat. 11, No. 6, 41-58 (2005).
Summary: We study properties of coefficients of a linear form originating from a multiple integral. As a corollary, we prove Vasil’ev’s conjecture, connected with the problem of irrationality of the Riemann zeta function at odd integers.
MSC:
11J72 Irrationality; linear independence over a field
11G55 Polylogarithms and relations with \(K\)-theory
11J82 Measures of irrationality and of transcendence
11M06 \(\zeta (s)\) and \(L(s, \chi)\)
33B30 Higher logarithm functions
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