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1 results

  • Arithmetic of singular moduli and class polynomials

  • Scott Ahlgren, Ken Ono
  • Journal:
    Compositio Mathematica / Volume 141 / Issue 2 / March 2005
    Published online by Cambridge University Press:
    10 February 2005, pp. 293-312
    Print publication:
    March 2005
    • Article
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  • 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 $j(z)| U_p\equiv 744 \pmod p$ (where $p\leq 11$ and j(z) is the usual modular invariant), and we investigate connections between class polynomials and supersingular polynomials in characteristic p.