Uniform asymptotic formulas for the Fourier coefficients of the inverse of theta functions
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 e...
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| Veröffentlicht in: | The Ramanujan journal 2022-03, Vol.57 (3), p.1085-1123 |
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| container_title | The Ramanujan journal |
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| creator | Liu, Zhi-Guo Zhou, Nian Hong |
| description | 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. |
| doi_str_mv | 10.1007/s11139-021-00409-8 |
| format | Article |
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| subjects | Asymptotic properties Combinatorics Field Theory and Polynomials Fourier Analysis Functions of a Complex Variable Mathematics Mathematics and Statistics Number Theory |
| title | Uniform asymptotic formulas for the Fourier coefficients of the inverse of theta functions |
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