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 t -modules. Our results are based on the intrinsic relations between gamma values in question and periods of CM dual t 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.