An explicit height bound for the classical modular polynomial

Reinier Bröker, Andrew V. Sutherland

Type: Article

Publication Date: 2010-04-21

Citations: 13

DOI: https://doi.org/10.1007/s11139-010-9231-8

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The Ramanujan Journal - View
arXiv (Cornell University) - View - PDF
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+	Class polynomials for nonholomorphic modular functions	2015	Jan Hendrik Bruinier Ken Ono Andrew V. Sutherland
+ PDF Chat	Degree and height estimates for modular equations on PEL Shimura varieties	2022	Jean Kieffer
+	Fonction thêta et applications à la cryptographie	2010	Damien Robert
+	On a simple model of X_0(N)	2017	Iva Kodrnja
+ PDF Chat	On the evaluation of modular polynomials	2013	Andrew V. Sutherland
+ PDF Chat	Modular polynomials via isogeny volcanoes	2011	Reinier Bröker Kristin Lauter Andrew V. Sutherland
+ PDF Chat	Upper bounds on the heights of polynomials and rational fractions from their values	2022	Jean Kieffer
+	On a pair of zeta functions	2016	Zhi‐Wei Sun
+ PDF Chat	Modular invariants and isogenies	2018	Fabien Pazuki
+ PDF Chat	On the distribution of Atkin and Elkies primes for reductions of elliptic curves on average	2015	Igor E. Shparlinski Andrew V. Sutherland

Works Cited by This (15)

Action	Title	Year	Authors
+	Analytic Number Theory	1973	Harold G. Diamond
+ PDF Chat	Introduction to Analytic Number Theory	1976	Tom M. Apostol
+	Weylsche Exponentialsummen in der neueren Zahlentheorie	1963	Arnold Walfisz
+ PDF Chat	Computing modular polynomials in quasi-linear time	2009	Andreas Enge
+ PDF Chat	Explicit estimates for summatory functions linked to the Möbius $\mu$-function	2007	Henri Cohen François Dress Mahomed El Marraki
+	The evaluation of Ramanujan’s sum and generalizations	1953	Douglas R. Anderson Tom M. Apostol
+	Elliptic and modular curves over finite fields and related computational issues	1997	Noam D. Elkies
+	On the coefficients of the transformation polynomials for the elliptic modular function	1984	Paula B. Cohen
+ PDF Chat	Computing Modular Polynomials	2005	Denis Charles Kristin Lauter
+	Analytic Number Theory	2004	Paul T. Bateman Harold G. Diamond