A Modular Form Proof of the Irrationality of $\zeta\left(3\right)$

Pang Ern Thang

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arXiv · 2607.17123

A Modular Form Proof of the Irrationality of $\zeta\left(3\right)$

Pang Ern Thang

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Abstract

We present an expository proof of the irrationality of $\zeta\left(3\right)$ using modular forms of level 6. By constructing a suitable Eichler integral, we obtain a power series with controlled denominators and sufficiently large radius of convergence. Beukers' irrationality criterion then implies that $\zeta\left(3\right)$ is irrational.

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Pang Ern Thang. 2026-07-19. A Modular Form Proof of the Irrationality of $\zeta\left(3\right)$. https://arxiv.org/abs/2607.17123

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