Determination of the algebraic relations among special $\Gamma$-values in positive characteristic

Abstract

We devise a new criterion for linear independence over function fields. Using this tool in the setting of dual $t$-motives, we find that all algebraic relations among special values of the geometric $\Gamma$-function over $\mathbb{F}_q[T]$ are explained by the standard functional equations.

Authors

Greg W. Anderson

Department of Mathematics
University of Minnesota
Minneapolis, MN 55455
United States

W. Dale Brownawell

Department of Mathematics
Pennsylvania State University
University Park, PA 16802
United States

Matthew Papanikolas

Department of Mathematics
Texas A & M University
College Station, TX 77843
United States