On Some Variants Of Schinzel's Theorem For Global Function Fields

TL;DR

This paper extends classical results of Schinzel and Postnikova, and Hahn and Cheon, to the setting of global function fields, providing new insights into multiplicative groups and elliptic curves.

Contribution

It introduces global function field analogs of existing theorems for multiplicative groups and elliptic curves, expanding their applicability.

Findings

Established function field versions of Schinzel - Postnikova results

Derived analogs of Hahn - Cheon results for elliptic curves

Enhanced understanding of algebraic structures over global function fields

Abstract

In this paper, we obtain global function field versions of the results of Schinzel - Postnikova for multiplicative groups, and of Hahn - Cheon for elliptic curves, which is an analog of the former result.