1. CMB 2005 (vol 48 pp. 147)
|Baker-Type Estimates for Linear Forms in the Values of $q$-Series |
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~$\II$, 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.
Keywords:measure of linear independence, $q$-series