Abstract

Abstract. We prove that the parity of the partition function is given by the “trace ” of the Hauptmodul j ∗ 6(z) for Γ ∗ 0(6) at points of complex multiplication. Using Hecke operators, we generalize this to relate the Hecke traces of j ∗ 6(z) to the partition function modulo 2. We then prove that the generating function for these Hecke traces is equal to the logarithmic derivative of the level 6 Hilbert class polynomial. Finally, we give a procedure involving Hilbert class polynomials for computing the parity of the partition function, and make some speculations about the distribution of these universal polynomials modulo class polynomials.

Citations