An explicit height bound for the classical modular polynomial

Details An explicit height bound for the classical modular polynomial An explicit height bound for the classical modular polynomial

2009-09-18

arxiv.org/abs/0909.3442v2

Ramanujan Journal 22 (2010), 293-313

Mathematics

Number Theory

Minor correction to the constants in Theorem 1 and Corollary 9. To appear in the Ramanujan Journal. 17 pages.

Scientific paper

For a prime m, let Phi_m be the classical modular polynomial, and let
h(Phi_m) denote its logarithmic height. By specializing a theorem of Cohen, we
prove that h(Phi_m) <= 6 m log m + 16 m + 14 sqrt m log m. As a corollary, we
find that h(Phi_m) <= 6 m log m + 18 m also holds. A table of h(Phi_m) values
is provided for m <= 3607.

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