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

  • Keijo Väänänen (a1) and Wadim Zudilin (a2)

Abstract

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.

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References

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

  • Keijo Väänänen (a1) and Wadim Zudilin (a2)

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