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arXiv · 1903.00835

Uniform asymptotic formulas for the Fourier coefficients of the inverse of theta functions

Zhi-Guo Liu·Nian Hong Zhou
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Abstract

In this paper, we use basic asymptotic analysis to establish some uniform asymptotic formulas for the Fourier coefficients of the inverse of Jacobi theta functions. In particular, we answer and improve some problems suggested and investigated by Bringmann, Manschot, and Dousse. As applications, we establish the asymptotic monotonicity properties for the rank and crank of the integer partitions introduced and investigated by Dyson, Andrews, and Garvan.

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Zhi-Guo Liu, Nian Hong Zhou. 2019-03-03. Uniform asymptotic formulas for the Fourier coefficients of the inverse of theta functions. https://arxiv.org/abs/1903.00835

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