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Arithmetic of singular moduli and class polynomials

By Scott Ahlgren and Ken Ono

Abstract

We investigate divisibility properties of the traces and Hecke traces of singular moduli. In particular we prove that, if p is prime, these traces satisfy many congruences modulo powers of p which are described in terms of the factorization of p in imaginary quadratic fields. We also study generalizations of Lehner’s classical congruences j(z)|Up ≡ 744 (mod p) (wherep � 11 and j(z) is the usual modular invariant), and we investigate connections between class polynomials and supersingular polynomials in characteristic p

Year: 2005
OAI identifier: oai:CiteSeerX.psu:10.1.1.134.6532
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