Gun–Ram Murty–Rath conjecture on logarithms of gamma values

For any positive integer $q>2$, let $\overline{V_{\Gamma}(q)}$ be the $\overline{\mathbb{Q}}$-vector space spanned by the real numbers

$$\log\Gamma\left(\frac{a}{q}\right),\qquad 1\leq a\leq q,\qquad (a,q)=1.$$

Gun–Ram Murty–Rath conjecture. The dimension of $\overline{V_{\Gamma}(q)}$ is

$$\dim_{\overline{\mathbb{Q}}}\overline{V_{\Gamma}(q)}=\phi(q).$$

This conjecture concerns the algebraic linear independence of logarithms of gamma values at reduced rational arguments and is relevant to the arithmetic nature of special values of derivatives of $L$-series and generalized Stieltjes constants. Its status is not resolved in the supplied source.