Milner 317

Wednesdays, 12:30-1:30 PM

University of Wisconsin

**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.