Baker-Type Estimates for Linear Forms in the Values of q-Series
Canadian mathematical bulletin, Tome 48 (2005) no. 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 $\mathbb{I}$ , 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.
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
@article{10_4153_CMB_2005_013_5,
author = {V\"a\"an\"anen, Keijo and Zudilin, Wadim},
title = {Baker-Type {Estimates} for {Linear} {Forms} in the {Values} of {q-Series}},
journal = {Canadian mathematical bulletin},
pages = {147--160},
year = {2005},
volume = {48},
number = {1},
doi = {10.4153/CMB-2005-013-5},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2005-013-5/}
}
TY - JOUR AU - Väänänen, Keijo AU - Zudilin, Wadim TI - Baker-Type Estimates for Linear Forms in the Values of q-Series JO - Canadian mathematical bulletin PY - 2005 SP - 147 EP - 160 VL - 48 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2005-013-5/ DO - 10.4153/CMB-2005-013-5 ID - 10_4153_CMB_2005_013_5 ER -
%0 Journal Article %A Väänänen, Keijo %A Zudilin, Wadim %T Baker-Type Estimates for Linear Forms in the Values of q-Series %J Canadian mathematical bulletin %D 2005 %P 147-160 %V 48 %N 1 %U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2005-013-5/ %R 10.4153/CMB-2005-013-5 %F 10_4153_CMB_2005_013_5
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