Identities for Anderson generating functions for Drinfeld modules

Abstract

Anderson generating functions are generating series for division values of points on Drinfeld modules, and they serve as important tools for capturing periods, quasi-periods, and logarithms. They have been fundamental in recent work on special values of positive characteristic $$L$$ -series and in transcendence and algebraic independence problems. In the present paper we investigate techniques for expressing Anderson generating functions in terms of the defining polynomial of the Drinfeld module and determine new formulas for periods and quasi-periods.