This article is cited in 4 papers

On linear independence of values of certain $q$-series

I. P. Rochev

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: We obtain qualitative and quantitative results on the linear independence of the values of functions in a fairly wide class generalizing $q$-hypergeometric series and of their derivatives at algebraic points. The results are proved in both the Archimedean and $p$-adic cases.

Keywords: algebraic number field, absolute height of an algebraic number, $q$-series, $q$-exponential function, $q$-logarithm, linear independence, linear independence measure, Hankel determinant, cyclotomic polynomial.

UDC: 511

MSC: 11J72, 11J82

Received: 26.11.2008
Revised: 22.10.2009

DOI: 10.4213/im4062

 English version: Izvestiya: Mathematics, 2011, 75:1, 177–221

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