Wednesday, November 30
Milner 317, 12:30 PM
Title: Maass-Poincare series and p-divisibility of traces of singular moduli
Abstract: Zagier initiated the study of traces of singular moduli Tr(d) and their generalizations as coefficients of certain weakly holomorphic half integral weight modular forms. We give a new proof of some of his identities which imply a new proof of the infinite product isomorphism announced by Borcherds in his 1994 ICM lecture. In addition, we discuss the p-adic properties of these traces and consequent congruences. In the case where p splits in Q(sqrt{-d}), we recover Edixhoven's observation that Tr(p^{2n} d) is congruent to 0 mod p^n.