# Susie Kimport

Affiliation: Stanford University

Email: skimport@stanford.edu

Title Of Talk: The asymptotics of partial theta functions

Abstract: Partial theta functions are sums whose terms resemble those of modular theta functions, save that the sums are taken over an incomplete lattice. In one of his notebooks, Ramanujan wrote down an asymptotic expansion for one particular partial theta functions as $q\to 1$. In 2011, Berndt and Kim generalized this type of asymptotic expansions to a related family, still for $q\to 1$. In this talk, we will extend the asymptotic results of Berndt and Kim to the case of $q\to e^{2\pi i h/k}$, any root of unity. In addition, we will present new asymptotic expansions of another family of partial theta functions.