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

Pages 237-313 from Volume 160 (2004), Issue 1 by Greg W. Anderson, W. Dale Brownawell, Matthew Papanikolas

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.

Mathematical Subject Classification

Primary 2000: Secondary: , ,

DOI
https://doi.org/10.4007/annals.2004.160.237
MR
2119721
zbMATH
1064.11055
Milestones
Received: 19 July 2002
Accepted: 9 December 2002
Published online: July 2004

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