Explicit Zsigmondy bounds for families of Drinfeld modules of rank 2

TL;DR

This paper establishes explicit bounds for Zsigmondy sets in specific families of rank 2 Drinfeld modules by analyzing local heights and relating them to classical heights.

Contribution

It provides the first explicit bounds for Zsigmondy sets in rank 2 Drinfeld modules, advancing understanding of their arithmetic properties.

Findings

Explicit bounds for Zsigmondy sets are derived.

A method relating local and classical heights is developed.

Results contribute to the arithmetic theory of Drinfeld modules.

Abstract

We give explicit bounds for Zsigmondy sets of certain families of Drinfeld modules of rank 2. The primary strategy is to bound the local heights associated to Drinfeld modules and then relate canonical to classical heights.