Good families of Drinfeld modular curves

TL;DR

This paper explores the properties of Drinfeld modular towers, demonstrating their optimality, providing explicit equations, and introducing a new optimal tower over a quadratic finite field.

Contribution

It introduces a new explicit example of an optimal Drinfeld modular tower and offers an algorithmic method to derive defining equations for such towers.

Findings

Identification of good and optimal Drinfeld modular towers

Development of an algorithm to compute explicit equations

Presentation of a new optimal tower over a quadratic finite field

Abstract

In this paper we investigate examples of good and optimal Drinfeld modular towers of function fields. Surprisingly, the optimality of these towers has not been investigated in full detail in the literature. We also give an algorithmic approach on how to obtain explicit defining equations for some of these towers and in particular give a new explicit example of an optimal tower over a quadratic finite field.