Is $\zeta(2n+1)\notin (2\pi)^{2n+1}\mathbb{Q}$ already known?

Question

Is it already shown or at least conjectured that $$\zeta(2n+1)\notin (2\pi)^{2n+1}\mathbb{Q}?$$

You have any names and years who proved or conjectured it?

Answer 1

The Wikipedia page on Apery's theorem (i.e. the irrationality of $\zeta(3)$) indicates $\zeta(2n+1)/(2\pi)^{2n+1}$ has been conjectured to be not merely irrational but transcendent. To this end they cite the following paper:

Kohnen, Winfried (1989). "Transcendence conjectures about periods of modular forms and rational structures on spaces of modular forms". Proc. Indian Acad. Sci. Math. Sci. 99 (3): 231–233. (This is available online through Springer here, but access is paywalled.)

Abstract: The conjecture is made that the rational structures on spaces of modular forms coming from the rationality of Fourier coefficients and the rationality of periods are not compatible. A consequence would be that $\zeta(2k-1)/π^{2k-1}$ ($\zeta(s)$=Riemann zeta function;$k\in\mathbb{N}$,$k\geq2$) is irrational or even transcendental.