Explicit Weil-pairing for Drinfeld Modules

TL;DR

This paper introduces an explicit Weil-pairing for Drinfeld modules, generalizing existing formulas for rank 2 and providing a more elementary proof of its properties.

Contribution

It develops an explicit formula for the Weil-pairing in Drinfeld modules, extending known results for rank 2 and simplifying the proof of its fundamental properties.

Findings

Explicit formula for Weil-pairing in Drinfeld modules

Generalization from rank 2 to higher ranks

Elementary proof of Weil-pairing properties

Abstract

The goal of this article is to define an analogue of the Weil-pairing for Drinfeld modules using explicit formulas and to deduce its main properties from these formulas. Our result generalizes the formula currently known for rank 2 Drinfeld modules and works as a more explicit, elementary proof of the Weil-pairing's existence than the one appearing in the current literature.