Algebraic Relations among Special Gamma Values and the Chowla-Selberg Phenomenon over Function Fields

The aim of this paper is to determine all algebraic relations among various special gamma values over function fields, and prove a Chowla-Selberg-type formula for quasi-periods of CM abelian $t$-modules. Our results are based on the intrinsic relations between gamma values in question and periods of CM dual $t$-motives, which are interpreted in terms of their "distributions". This also enables us to derive an analogue of the Deligne-Gross period conjecture for CM Hodge-Pink structures.