3 changed the language to be less of an endorsement of the cited work

Someone recently quoted to me this recent article that proves 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

2 corrected a typo. thx to Pete L Clark; added 45 characters in body

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

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

1

# Values of zeta at odd positive integers and Borel's computations

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

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?