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


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.


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