Asymptotics of generalized partial theta functions with a Dirichlet character

TL;DR

This paper derives asymptotic expansions for generalized partial theta functions involving nonprincipal Dirichlet characters and connects these expansions to specific $L$-series, advancing understanding in analytic number theory.

Contribution

It provides the first detailed asymptotic analysis of generalized partial theta functions with nonprincipal Dirichlet characters and links these to $L$-series.

Findings

Asymptotic expansions for generalized partial theta functions with nonprincipal Dirichlet characters.

Connections established between these expansions and certain $L$-series.

Enhanced understanding of the analytic properties of these functions.

Abstract

In this paper, we prove asymptotic expansions of generalized partial theta functions with a nonprincipal Dirichlet character and relate these expansions to certain $L$-series.