Reduction of CM elliptic curves and modular function congruences

dc.creatorElkies, Noam D.
dc.creatorOno, Ken
dc.creatorYang, Tonghai
dc.date2005-12-15
dc.date.accessioned2026-07-07T06:55:19Z
dc.date.available2026-07-07T06:55:19Z
dc.descriptionWe 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.
dc.description11 pages
dc.identifierhttps://arxiv.org/abs/math/0512350
dc.identifierhttp://arxiv.org/abs/math/0512350
dc.identifierInternational Math. Research Notices, Vol. 2005, #44, pages 2695--2707
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/106242
dc.subjectNumber Theory
dc.subject11F33 (11G05; 11G15)
dc.titleReduction of CM elliptic curves and modular function congruences
dc.typetext

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