On sums of S-integers of bounded norm

TL;DR

This paper derives an asymptotic formula for counting S-integers in a number field that can be expressed as sums of a fixed number of S-integers with bounded norm.

Contribution

It provides a new asymptotic count for representations of S-integers as sums of bounded norm S-integers in number fields.

Findings

Established an asymptotic formula for the count

Extended understanding of S-integer representations

Applicable to various number fields

Abstract

We prove an asymptotic formula for the number of S-integers in a number field K that can be represented by a sum of n S-integers of bounded norm.