Publication: Reduction of CM elliptic curves and modular function congruences
Open/View Files
Date
2005
Authors
Published Version
Published Version
Journal Title
Journal ISSN
Volume Title
Publisher
The Harvard community has made this article openly available. Please share how this access benefits you.
Citation
Elkies, Noam D., Ken Ono, and Tonghai Yang. 2005. Reduction of CM elliptic curves and modular function congruences. International Mathematics Research Notices (44): 2695-2707.
Research Data
Abstract
We study congruences of the form F(j(z)) | U(p) = G(j(z)) mod p, where U(p) is the p-th Hecke operator, j is the basic modular invariant 1/q+744+196884q+... for SL2(Z), and F,G are polynomials with integer coefficients. Using the interplay between singular (a.k.a. CM) j-invariants in characteristic zero and supersingular ones in characteristic p, we obtain such congruences in which F is the minimal polynomial of a CM j-invariant, and give a sufficient condition for G to be a constant polynomial in these congruences.
Description
Other Available Sources
Keywords
quadratic forms, singular moduli, half-integral weight
Terms of Use
This article is made available under the terms and conditions applicable to Other Posted Material (LAA), as set forth at Terms of Service