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

of courseyou're welcome to doubt the validity of someone's article that you haven't seen, for any reason. [Was there anything in what I wrote that made you think that I have confidence in Musha's result?] It is not always appropriate or wise to publicly express every opinion you have. $\endgroup$ – Pete L. Clark Sep 10 '10 at 5:18