Reduction of CM elliptic curves and modular function congruences
| dc.creator | Elkies, Noam D. | |
| dc.creator | Ono, Ken | |
| dc.creator | Yang, Tonghai | |
| dc.date | 2005-12-15 | |
| dc.date.accessioned | 2026-07-07T06:55:19Z | |
| dc.date.available | 2026-07-07T06:55:19Z | |
| dc.description | 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. | |
| dc.description | 11 pages | |
| dc.identifier | https://arxiv.org/abs/math/0512350 | |
| dc.identifier | http://arxiv.org/abs/math/0512350 | |
| dc.identifier | International Math. Research Notices, Vol. 2005, #44, pages 2695--2707 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/106242 | |
| dc.subject | Number Theory | |
| dc.subject | 11F33 (11G05; 11G15) | |
| dc.title | Reduction of CM elliptic curves and modular function congruences | |
| dc.type | text |