On Furusho's analytic continuation of Drinfeld logarithms

TL;DR

This paper extends Drinfeld logarithms analytically using techniques from Fur20, paralleling elliptic integral continuation, and provides new insights into their complex analytic structure.

Contribution

It introduces an analytic continuation method for Drinfeld logarithms, advancing the understanding of their complex analytic properties.

Findings

Established an analytic continuation for Drinfeld logarithms.

Draws an analogy with elliptic integrals of the first kind.

Provides a new perspective on Drinfeld modules' complex analysis.

Abstract

In the present paper, we establish an analytic continuation of Drinfeld logarithms by using the techniques introduced in [Fur20]. This result can be seen as an analogue of the analytic continuation of the elliptic integrals of the first kind for Drinfeld modules.