Bivariate asymptotics for eta-theta quotients with simple poles

TL;DR

This paper develops a bivariate asymptotic analysis for Fourier coefficients of eta-theta quotients with simple poles, using a modified Wright's circle method to handle complex poles in the upper half-plane.

Contribution

It introduces a novel application of Wright's circle method to derive bivariate asymptotics for eta-theta quotients with simple poles.

Findings

Derived explicit asymptotic formulas for Fourier coefficients.

Extended Wright's circle method to handle eta-theta quotients with poles.

Provided insights into the growth behavior of these Fourier coefficients.

Abstract

We employ a variant of Wright's circle method to determine the bivariate asymptotic behaviour of Fourier coefficients for a wide class of eta-theta quotients with simple poles in $\mathbb{H}$.