A lower bound for the canonical height on elliptic curves over abelian extensions |
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Authors: | Joseph H Silverman |
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Institution: | Mathematics Department, Box 1917, Brown University, Providence, RI 02912, USA |
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Abstract: | Let E/K be an elliptic curve defined over a number field, let ? be the canonical height on E, and let Kab/K be the maximal abelian extension of K. Extending work of M. Baker (IMRN 29 (2003) 1571-1582), we prove that there is a constant C(E/K)>0 so that every nontorsion point P∈E(Kab) satisfies . |
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Keywords: | primary: 11G05 secondary: 11G10 14G25 14K15 |
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