Transcendence of special values of log double sine function
Hidekazu Tanaka · Proceedings of the Japan Academy Series A Mathematical Sciences · 2014
In 2009~[4,5], S. Gun, M. R. Murty, P. Rath studied transcendental values of the logarithm of the gamma function. They showed that for any rational number $x$ with $0 < x < \frac{1}{2}$, the number $\log \Gamma(x) + \log \Gamma(1-x)$ is transcendental with at most one possible exception. In this paper, we study transcendental values of log double sine function using their method.