Sharon Garthwaite

Affiliation: Bucknell University

Email: sag028@bucknell.edu

Title Of Talk: Weakly Holormorphic Modular Forms Arising from Theta Series

Abstract: In 1920 Ramanujan introduced the world to mock theta functions, $q$-series with strange analytic and transformation properties.These functions, for example, $f(q)$ and $\omega(q)$, naturally arise in the study of partitions, and, more recently, the study of rank moments. In 2003 S. P. Zwegers gave us the first hint to understanding the transformation properties of these functions by looking at forms ``completed'' with period integrals of theta series.K. Bringmann and K. Ono built upon this work to place these mock theta functions into the framework of automorphic forms, specifically harmonic weak Maass forms. Bringmann, Ono, and R. Rhoades have built infinite families of harmonic weak Maass forms involving period integrals of theta series of weight 1/2 and 3/2. In this talk we will explore the "holomorphic part" of these functions. This is joint work with David Penniston of Furman University.

Last update made Wed Feb 13 22:25:28 EST 2008.
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