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

TL;DR

This paper investigates algebraic relations among special gamma values over function fields, establishing a Chowla-Selberg-type formula for quasi-periods of CM abelian t-modules and connecting gamma values with periods of CM dual t-motives.

Contribution

It provides a complete description of algebraic relations among gamma values and proves a Chowla-Selberg-type formula in the function field setting, linking gamma values to periods of CM dual t-motives.

Findings

Algebraic relations among special gamma values are fully characterized.

A Chowla-Selberg-type formula for quasi-periods of CM abelian t-modules is established.

An analogue of the Deligne-Gross period conjecture for CM Hodge-Pink structures is derived.

Abstract

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.