Simplest quartic and simplest sextic Thue equations over imaginary quadratic fields

TL;DR

This paper extends the study of simplest quartic and sextic Thue equations to imaginary quadratic fields, providing explicit solutions for these infinite families over such fields.

Contribution

It introduces explicit solutions for simplest quartic and sextic Thue equations over imaginary quadratic fields, expanding previous work on cubic cases.

Findings

Explicit solutions for infinite families of Thue equations over imaginary quadratic fields.

Extension of known results from cubic to quartic and sextic cases.

Provides a comprehensive framework for solving these equations in the specified fields.

Abstract

The families of simplest cubic, simplest quartic and simplest sextic fields and the related Thue equations are well known. The family of simplest cubic Thue equations was already studied in the relative case, over imaginary quadratic fields. In the present paper we give a similar extension of simplest quartic and simplest sextic Thue equations over imaginary quadratic fields. We explicitly give the solutions of these infinite parametric families of Thue equations over arbitrary imaginary quadratic fields.