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Automorphic properties of combinatorial generating functions

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An intriguing and almost completely unsolved problem is to understand the overlap between classes of q-hypergeometric series and automorphic forms. For example, we now know that each of Ramanujan’s mock theta functions is the holomorphic part of a weak Maass form. In this talk, we provide a framework which generalizes recent work of Andrews and discuss automorphic properties of the associated q-hypergeometric series. This is joint work with Kathrin Bringmann and Jeremy Lovejoy.

This talk is part of the Number Theory Seminar series.

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