An alternative proof of the asymptotic formula for the Fourier coefficients of the elliptic modular $j$-function
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909840156131328 |
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| author | Ikeda, Karin |
| author_facet | Ikeda, Karin |
| contents | In 1997, Báez-Duarte gave a probabilistic proof of the asymptotic formula for the partition function, which had originally been proved by Hardy-Ramanujan. Based on the probabilistic approach, this paper proves an asymptotic formula for the coefficients of the elliptic modular $j$-function using various expressions in terms of modular functions having simple infinite products. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_10598 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An alternative proof of the asymptotic formula for the Fourier coefficients of the elliptic modular $j$-function Ikeda, Karin Number Theory 11F30, 11F03, 60F05 In 1997, Báez-Duarte gave a probabilistic proof of the asymptotic formula for the partition function, which had originally been proved by Hardy-Ramanujan. Based on the probabilistic approach, this paper proves an asymptotic formula for the coefficients of the elliptic modular $j$-function using various expressions in terms of modular functions having simple infinite products. |
| title | An alternative proof of the asymptotic formula for the Fourier coefficients of the elliptic modular $j$-function |
| topic | Number Theory 11F30, 11F03, 60F05 |
| url | https://arxiv.org/abs/2510.10598 |