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Asymptotics for nonmodular infinite products

In this talk, I will present an investigation ofasymptotics near rational points on the unit circle for nonmodular infiniteproducts. More precisely, our attention is focused on infinite products of theform $1/(q^a;q^M)_\infty$ where $M$ is a positive integer and $a$ is any of$1,2,\ldots,M$. Such asymptotic expansions will be used to tackle a conjectureof S. Seo and A. J. Yee.

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