Catalan's constant is irrational

Zhi-Wei Sun

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arXiv · 2609.04176

Catalan's constant is irrational

Zhi-Wei Sun

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Abstract

Whether the constant $$G=\sum_{k=0}^\infty\frac{(-1)^k}{(2k+1)^2}=\frac1{1^2}-\frac1{3^2}+\frac1{5^2}-\frac1{7^2}+\cdots$$ introduced by Catalan in the nineteen century is irrational, is a long-standing open problem. In this paper we prove the irrationality of $G$ via using suitable weights.

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Zhi-Wei Sun. 2026-09-03. Catalan's constant is irrational. https://arxiv.org/abs/2609.04176

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