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University of South Carolina
Title:Integer weight mock theta analogues.
Abstract: Recent work of Bringmann and Ono explains how the "mock theta" functions of Ramanujan fit in the broader theory of automorphic forms. While a mock theta function F(q) is not a modular form, by adding to it the period integral of a suitable theta series (a modular form of half-integral weight 1/2 or 3/2), we obtain a harmonic weak Maass form. Since period integrals of modular forms are non-holomorphic, we say that the mock theta function is the "holomorphic part" of the resulting Maass form. In this talk, we discuss harmonic weak Maass forms whose non-holomorphic parts are given by period integrals of modular forms of integer weight like the classical Delta function. We will study arithmetic properties of the holomorphic parts, which play the role of "mock theta"-type functions in this setting.