Wikipedia mentions that the transcendence of $\Gamma(1/3), \Gamma(1/4)$ was proved by G. V. Chudnovsky. Does anyone have a reference to that proof? Or maybe some details on the essential ideas involved in the proof would be greatly helpful.
Also is there any simpler proof available when we want the conclusion to just "irrationality" instead of "transcendence"?
Update: I posted this at MO also and got the reference I wanted.