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Baker-Type Estimates for Linear Forms in the Values of q-Series

Published online by Cambridge University Press:  20 November 2018

Keijo Väänänen  and
Wadim Zudilin
Keijo Väänänen
Affiliation:
University of Oulu, Department of Mathematical Sciences, P. O. Box 3000, 90014 Oulun Yliopisto, Finland e-mail: kvaanane@sun3.oulu.fi
Wadim Zudilin
Affiliation:
Moscow Lomonosov State University, Department of Mechanics and Mathematics, Vorobiovy Gory, GSP-2, 119992 Moscow, Russia e-mail: wadim@ips.ras.ru
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Abstract

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We obtain lower estimates for the absolute values of linear forms of the values of generalized Heine series at non-zero points of an imaginary quadratic field $\mathbb{I}$, in particular of the values of $q$-exponential function. These estimates depend on the individual coefficients, not only on the maximum of their absolute values. The proof uses a variant of classical Siegel's method applied to a system of functional Poincaré-type equations and the connection between the solutions of these functional equations and the generalized Heine series.

Keywords

11J8233D15measure of linear independenceq-series
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 48 , Issue 1 , 01 March 2005 , pp. 147 - 160
Copyright
Copyright © Canadian Mathematical Society 2005

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