Transcendence in positive characteristic and special values of hypergeometric functions

We prove a simple transcendence criterion suitable for function field arithmetic. We apply it to show the transcendence of special values at non-zero rational arguments (or more generally, at algebraic arguments which generate extension of the rational function field with less than q places at infinity) of the entire hypergeometric functions in the function field (over F(q)) context, and to obtain a new proof of the transcendence of special values at non-natural p-adic integers of the Carlitz-Goss gamma function. We also characterize in the balanced case the algebraicity of hypergeometric functions, giving an analog of the result of F. R. Villegas, based on Beukers-Heckman results and E. Landau's method in the classical hypergeometric case.