A Measure of Simultaneous Approximation for Quasi-Modular Functions |
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Authors: | Grinspan Pierre |
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Affiliation: | (1) Institut de Mathématiques, Université de Paris VI, Théorie des Nombres, Case 247, 175 Rue du Chevaleret, 75013 Paris, France |
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Abstract: | We improve on a recent result of Saradha giving a transcendence measure for the quotient of a period of an elliptic curve defined over by its associated quasi-period. In an (almost successful) attempt to include in a single measure both this result and that obtained by Reyssat in 1980, we blend into the modular method ideas related to modular but also hypergeometric functions, as appearing e.g. in André's work, as well as some Galois considerations. |
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Keywords: | gamma function hypergeometric series modular forms theta functions approximation measures simultaneous approximation transcendence measures |
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