(1) Can anybody suggest a readable reference for Schneider's theorem that the number $$ \beta(a, b)=\frac{\Gamma(a)\Gamma(b)}{\Gamma(a+b)} $$ is transcendental for $a, b \in \mathbb{Q}$ such that none of $a, b, a+b$ is an integer?

(2) Fix some integer $n \geq 3$ Is the degree of transcendence of the field generated over $\mathbb{Q}$ by $$ \left(\beta(\tfrac{i}{d}, \tfrac{j}{d})\right)_{i, j=1, \ldots, d-1} $$ known?


Scheider's original paper is available online. The theorem you quote is proved at the end of Section 1, on Page 114. I don't know the answer to your second question, but my guess is "no".

| cite | improve this answer | |
  • $\begingroup$ Thanks for the paper! Do you know other places where this is proved e.g. not in German? :) $\endgroup$ – schn93 Sep 19 '14 at 6:51

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.