Geodesic
Baker-Type Estimates for Linear Forms in the Values of q-Series
Canadian mathematical bulletin, Tome 48 (2005) no. 1, pp. 147-160

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CMB-2005-013-5
Mots-clés : 11J82, 33D15, measure of linear independence, q-series 
Väänänen, Keijo; Zudilin, Wadim. Baker-Type Estimates for Linear Forms in the Values of q-Series. Canadian mathematical bulletin, Tome 48 (2005) no. 1, pp. 147-160. doi: 10.4153/CMB-2005-013-5
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