Arithmetic of singular moduli and class polynomials

Scott Ahlgren, Ken Ono

Research output: Contribution to journalArticlepeer-review


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) (where p ≤ 11 and j(z) is the usual modular invariant), and we investigate connections between class polynomials and supersingular polynomials in characteristic p.

Original languageEnglish (US)
Pages (from-to)293-312
Number of pages20
JournalCompositio Mathematica
Issue number2
StatePublished - 2005


  • Class polynomials
  • Modular forms
  • Singular moduli

ASJC Scopus subject areas

  • Algebra and Number Theory


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