An alternative proof of the asymptotic formula for the Fourier coefficients of the elliptic modular $j$-function

Karin Ikeda

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arXiv · 2510.10598

An alternative proof of the asymptotic formula for the Fourier coefficients of the elliptic modular $j$-function

Karin Ikeda

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Abstract

In 1997, B\'aez-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.

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Karin Ikeda. 2025-10-12. An alternative proof of the asymptotic formula for the Fourier coefficients of the elliptic modular $j$-function. https://arxiv.org/abs/2510.10598

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