  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.
