A note on Gekeler's h-function

TL;DR

This paper explores Drinfeld modular forms, focusing on the h-function, offering new characterizations using Moore determinants, and applying these to the Weil pairing, while also defining modular functions of non-zero type with moduli interpretation.

Contribution

It introduces new characterizations of the h-function via Moore determinants and extends the theory to modular functions of non-zero type with a moduli perspective.

Findings

New characterizations of the h-function using Moore determinants

Application of these characterizations to the Weil pairing

Definition and moduli interpretation of non-zero type Drinfeld modular functions

Abstract

We give a brief introduction to Drinfeld modular forms, concentrating on the many equivalent constructions of the form h of weight q+1 and type 1, to which we contribute some new characterizations involving Moore determinants, and an application to the Weil pairing on Drinfeld modules. We also define Drinfeld modular functions of non-zero type and provide a moduli interpretation of these.