An explicit height bound for the classical modular polynomial |
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| Authors: | Reinier Bröker Andrew V Sutherland |
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| Institution: | (1) Institute of Mathematics and Informatics, Akademijos 4, 2600 Vilnius, Lithuania;(2) Department of Mathematics and Informatics, Vilnius University, Naugarduko 24, 2600 Vilnius, Lithuania |
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| Abstract: | For a prime l, let Φ l be the classical modular polynomial, and let h(Φ l ) denote its logarithmic height. By specializing a theorem of Cohen, we prove that \(h(\Phi_{l})\le 6l\log l+16l+14\sqrt{l}\log l\). As a corollary, we find that h(Φ l )≤6llog?l+18l also holds. A table of h(Φ l ) values is provided for l≤3600. |
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