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Tuesday, December 10, 2013

**Abstract:** It is well-known that the values of the partition function p(n) appear as the coefficients of a modular form. In my talk, I will show how we can construct a mock modular form whose "shadow" encodes the partition function, and whose coefficients are given by inner products of the partition generating function and other modular forms of weight -1/2. On the way, we will encounter Rademacher's exact formula for p(n). I will also show how this mock modular form is one member of an infinite basis for the space of mock modular forms of weight 5/2 on the full modular group. This is joint work with Scott Ahlgren.