Quantum mock modular forms arising from eta-theta functions
Title: Quantum mock modular forms arising from eta-theta functions
Speaker: Professor Amanda Folsom (Amherst College and
MPIM, Bonn)
Date: Monday, 16th November 2015
Time: 4pm
Location: Agriculture. 1.01 (Seminar Room).
Abstract:
Lemke-Oliver classified all modular eta-quotients which are also theta functions; we denote the set of such functions by A. In joint work with Garthwaite, Swisher, and Treneer, we construct mock modular forms using a subset B of these eta-theta functions. Moreover, we show that these mock modular forms have shadows which are given by the eta-theta functions in the complementary subset A\B. We further prove that some of our mock modular forms arising from eta-theta functions in this way are also quantum modular forms. As corollaries, we explicitly evaluate Eichler integrals of eta-theta functions as finite q-hypergeometric sums, and establish related curious algebraic identities.
Series: Algebra and Number Theory
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