Asymptotics for the Fourier coefficients of eta-quotients

Abstract

We study the asymptotics for the Fourier coefficients of a broad class of eta-quotients, $$\prod _{r=1}^R{\left(\prod _{k\ge 1}\left(1-q^{m_{r}k}\right)\right)}^{\hat{I}{´}_r},$$ where $m_1,\dots ,m_R$ are $R$ distinct positive integers and $\hat{I}{´}_1,\dots ,\hat{I}{´}_R$ are $R$ non-zero integers with ${\sum }_{r=1}^R\hat{I}{´}_r\ge 0$.