Baker-type estimates for linear forms in the values of q-series

V\"a\"anä, Keijo and Zudilin, Wadim (2005) Baker-type estimates for linear forms in the values of q-series. Canadian Mathematical Society, 48 (1). pp. 147-160.

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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 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 Poincar´e-type equations and the connection between the solutions of these functional equations and the generalized Heine series.

Item Type: Article
Uncontrolled Keywords: measure of linear independence, q-series, Baker-type estimates
Depositing User: Dr David Allingham
Date Deposited: 28 Sep 2012 12:05
Last Modified: 28 Sep 2012 12:05

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