Identities for Anderson generating functions for Drinfeld modules

TL;DR

This paper explores methods to express Anderson generating functions for Drinfeld modules using their defining polynomials, providing new formulas for periods and quasi-periods, which are vital in number theory and transcendence studies.

Contribution

It introduces novel techniques to relate Anderson generating functions to the defining polynomials of Drinfeld modules and derives new formulas for fundamental invariants.

Findings

New formulas for periods and quasi-periods of Drinfeld modules

Techniques for expressing Anderson generating functions in terms of defining polynomials

Enhanced understanding of special values in positive characteristic L-series

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.