Rational integers as sums of units -- the quadratic case
Number Theory
2026-01-15 v1
Abstract
How many natural numbers below can be written as a sum of units of the ring of integers of a given number field? We give the asymptotics as gets large for quadratic number fields. This solves a problem of Jarden and Narkiewicz from 2007 for quadratic number fields.
Cite
@article{arxiv.2601.09517,
title = {Rational integers as sums of units -- the quadratic case},
author = {Christopher Frei and Martin Widmer and Volker Ziegler},
journal= {arXiv preprint arXiv:2601.09517},
year = {2026}
}
Comments
14 pages; comments welcome!