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Someone recently quoted to me this recent article that claims to prove that $\zeta(2n+1) \notin (2\pi )^{2n+1} \mathbb{Q}$.

I always assumed this was well known. More precisely I thought this result followed from the fact that the regulator $$ K_{2n-1}(\mathbb{Z})\otimes \mathbb{Q} = Ext^1_{MT(\mathbb{Z})}(\mathbb{Q}(0),\mathbb{Q}(n)) \longrightarrow Ext^1_{MHS}(\mathbb{Q}(0),\mathbb{Q}(n)) = \mathbb{C}/(2\pi i)^n\mathbb{Q} $$ is injective (this is usually quoted as a consequence of Borel's computations of K-groups "Stable real cohomology of arithmetic groups", "Cohomologie de $SL_n$ et valeurs de fonctions zêta aux points entiers")

Am I mistaken?

PS: corrected a typo thx to Pete L Clark

Someone recently quoted to me this recent article that claims to prove that $\zeta(2n+1) \notin (2\pi )^{2n+1} \mathbb{Q}$.

[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).]

I always assumed this was well known. More precisely I thought this result followed from the fact that the regulator $$ K_{2n-1}(\mathbb{Z})\otimes \mathbb{Q} = \operatorname{Ext}^1_{MT(\mathbb{Z})}(\mathbb{Q}(0),\mathbb{Q}(n)) \longrightarrow \operatorname{Ext}^1_{MHS}(\mathbb{Q}(0),\mathbb{Q}(n)) = \mathbb{C}/(2\pi i)^n\mathbb{Q} $$ is injective (this is usually quoted as a consequence of Borel's computations of K-groups "Stable real cohomology of arithmetic groups", "Cohomologie de $\operatorname{SL}_n$ et valeurs de fonctions zêta aux points entiers")

Am I mistaken?

Someone recently quoted to me this recent article that claims to prove that $\zeta(2n+1) \notin (2\pi )^{2n+1} \mathbb{Q}$.

I always assumed this was well known. More precisely I thought this result followed from the fact that the regulator $$ K_{2n-1}(\mathbb{Z})\otimes \mathbb{Q} = Ext^1_{MT(\mathbb{Z})}(\mathbb{Q}(0),\mathbb{Q}(n)) \longrightarrow Ext^1_{MHS}(\mathbb{Q}(0),\mathbb{Q}(n)) = \mathbb{C}/(2\pi i)^n\mathbb{Q} $$ is injective (this is usually quoted as a consequence of Borel's computations of K-groups "Stable real cohomology of arithmetic groups", "Cohomologie de $SL_n$ et valeurs de fonctions zêta aux points entiers")

Am I mistaken?

PS: corrected a typo thx to Pete L Clark

Someone recently quoted to me this recent article that claims to prove that $\zeta(2n+1) \notin (2\pi )^{2n+1} \mathbb{Q}$.

I always assumed this was well known. More precisely I thought this result followed from the fact that the regulator $$ K_{2n-1}(\mathbb{Z})\otimes \mathbb{Q} = Ext^1_{MT(\mathbb{Z})}(\mathbb{Q}(0),\mathbb{Q}(n)) \longrightarrow Ext^1_{MHS}(\mathbb{Q}(0),\mathbb{Q}(n)) = \mathbb{C}/(2\pi i)^n\mathbb{Q} $$ is injective (this is usually quoted as a consequence of Borel's computations of K-groups "Stable real cohomology of arithmetic groups", "Cohomologie de $SL_n$ et valeurs de fonctions zêta aux points entiers")

Am I mistaken?

PS: corrected a typo thx to Pete L Clark

Someone recently quoted to me this recent article that proves that $\zeta(2n+1) \notin (2\pi )^{2n+1} \mathbb{Q}$.

I always assumed this was well known. More precisely I thought this result followed from the fact that the regulator $$ K_{2n-1}(\mathbb{Z})\otimes \mathbb{Q} = Ext^1_{MT(\mathbb{Z})}(\mathbb{Q}(0),\mathbb{Q}(n)) \longrightarrow Ext^1_{MHS}(\mathbb{Q}(0),\mathbb{Q}(n)) = \mathbb{C}/(2\pi i)^n\mathbb{Q} $$ is injective (this is usually quoted as a consequence of Borel's computations of K-groups "Stable real cohomology of arithmetic groups", "Cohomologie de $SL_n$ et valeurs de fonctions zêta aux points entiers")

Am I mistaken?

PS: corrected a typo thx to Pete L Clark

Someone recently quoted to me this recent article that claims to prove that $\zeta(2n+1) \notin (2\pi )^{2n+1} \mathbb{Q}$.

I always assumed this was well known. More precisely I thought this result followed from the fact that the regulator $$ K_{2n-1}(\mathbb{Z})\otimes \mathbb{Q} = Ext^1_{MT(\mathbb{Z})}(\mathbb{Q}(0),\mathbb{Q}(n)) \longrightarrow Ext^1_{MHS}(\mathbb{Q}(0),\mathbb{Q}(n)) = \mathbb{C}/(2\pi i)^n\mathbb{Q} $$ is injective (this is usually quoted as a consequence of Borel's computations of K-groups "Stable real cohomology of arithmetic groups", "Cohomologie de $SL_n$ et valeurs de fonctions zêta aux points entiers")

Am I mistaken?

PS: corrected a typo thx to Pete L Clark