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Thursday, February 17, 2005

**Abstract:** Recent works have used the theory of modular forms to establish linear congruences for the partition function and for traces of singular moduli. We show that this type of phenomena is completely general, by finding similar congruences for the coefficients of any weakly holomorphic modular form. In particular, we give congruences for a wide class of partitions functions and for traces of CM values of arbitrary modular functions on certain congruence subgroups of prime level. Tuesday's talk will consist of an introduction to the problem, a statement of the main theorems, and a discussion of the two applications. Thursday we will prove the main theorems.