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In this article, Takaaki Musha proves that $\zeta(2n+1) \notin (2\pi )^{2n+1} \mathbb{Q}$. I haven't read it so I can't say more.

[Edit: published reference: Musha, Takaaki. Negation of the conjecture for odd zeta values. Int. J. Pure Appl. Math. 91, No. 1, 103-111 (2014). Not referenced by MathSciNet, and referenced by zbMATH (link).]

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In the below article Takaaki Musha claims a proof that $\zeta(2n+1) \notin (2\pi )^{2n+1} \mathbb{Q}$. I haven't read it so I can't say more.

• Musha, Takaaki. Negation of the conjecture for odd zeta values. Int. J. Pure Appl. Math. 91, No. 1, 103-111 (2014) doi:10.12732/ijpam.v91i1.11, zbMATH entry.

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In this article, Takaaki Musha proves that $\zeta(2n+1) \notin (2\pi )^{2n+1} \mathbb{Q}$. I haven't read it so I can't say more.

See this question.

In this article, Takaaki Musha proves that $\zeta(2n+1) \notin (2\pi )^{2n+1} \mathbb{Q}$. I haven't read it so I can't say more.

[Edit: published reference: Musha, Takaaki. Negation of the conjecture for odd zeta values. Int. J. Pure Appl. Math. 91, No. 1, 103-111 (2014). Not referenced by MathSciNet, and referenced by zbMATH (link).]

See this question.

In this article, Takaaki Musha proves that $\zeta(2n+1) \notin (2\pi )^{2n+1} \mathbb{Q}$. I haven't read it so I can't say more.

See this question.

In this article, Takaaki Musha proves that $\zeta(2n+1) \notin (2\pi )^{2n+1} \mathbb{Q}$. I haven't read it so I can't say more.

See this question.