Abstract
Let E be an elliptic curve with complex multiplication, defined over Q . We consider linear forms on Lie( E n) with coefficients in the CM field of E . Within this framework, we present a new measure of linear independence for elliptic logarithms in (log b)(log a) n . Like recent advances in this domain (works by Ably, David, Hirata-Kohno), our result is best possible in terms of the height of the linear forms (log b) while providing a better estimate in the height of algebraic points considered (log a), removing a term in loglog a. To cite this article: M. Ably, É. Gaudron, C. R. Acad. Sci. Paris, Ser. I 337 (2003).
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