Transcendence of Gamma values for F_q[T], by Dinesh S. Thakur

This paper has appeared in Ann. of Math. (2) 144 (1996), no. 1, 181-188, and so the dvi version has been removed. We prove that many gamma values at proper fractions of the Gamma function for F_q[T] (introduced by Carlitz and Goss) are transcendental over F_q(T). In particular, (n-1/b)! is transcendental for any integer n and a positive integer b>1 and prime to q. Our proof is based on transcendence criterion of Christol.

Dinesh S. Thakur <thakur@math.arizona.edu>