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