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

• Autores: Keijo Väänänen, Wadim Zudilin
• Localización: Canadian mathematical bulletin, ISSN 0008-4395, Vol. 48, Nº 1, 2005, págs. 147-160
• Idioma: inglés
• DOI: 10.4153/cmb-2005-013-5
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• Resumen

  • 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 Poincaré-type equations and the connection between the solutions of these functional equations and the generalized Heine series.