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Padé Approximations and Diophantine Geometry

D. V. Chudnovsky and G. V. Chudnovsky
Proceedings of the National Academy of Sciences of the United States of America
Vol. 82, No. 8 (Apr. 15, 1985), pp. 2212-2216
Stable URL: http://www.jstor.org/stable/25067
Page Count: 5
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Padé Approximations and Diophantine Geometry
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Abstract

Using methods of Padé approximations we prove a converse to Eisenstein's theorem on the boundedness of denominators of coefficients in the expansion of an algebraic function, for classes of functions, parametrized by meromorphic functions. This result is applied to the Tate conjecture on the effective description of isogenies for elliptic curves.

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