An explicit height bound for the classical modular polynomial

作者：Broeker Reinier; Sutherland Andrew V^*

来源：Ramanujan Journal, 2010, 22(3): 293-313.

DOI：10.1007/s11139-010-9231-8

• Modular polynomials
• Height bounds
• j-function

For a prime l, let Phi(l) be the classical modular polynomial, and let h(Phi(l)) denote its logarithmic height. By specializing a theorem of Cohen, we prove that h(Phi(l)) <= 6l log l + 16l + 14 root l logl. As a corollary, we find that h(Phi(l)) <= 6l log l + 18l also holds. A table of h(Phi(l)) values is provided for l <= 3600.

• 出版日期2010-8