On the maximum modulus of integers in Kummer extensions

TL;DR

This paper extends a classical result on representing algebraic integers as sums of roots of unity to the broader context of Kummer extensions, providing new insights into their maximum modulus properties.

Contribution

It generalizes Loxton's 1972 result from cyclotomic fields to Kummer extensions, expanding understanding of algebraic integer representations.

Findings

Extended bounds on the maximum modulus of integers in Kummer extensions

Provided new methods for representing algebraic integers as sums of roots of unity

Enhanced theoretical framework for algebraic number representations

Abstract

We study the extension of a result of Loxton (1972) on representation of algebraic integers as sums of roots of unity to Kummer extensions.