Rational integers as sums of units -- the quadratic case

preprint2026arXivOpen access

How many natural numbers below $X$ can be written as a sum of $k$ units of the ring of integers of a given number field? We give the asymptotics as $X$ gets large for quadratic number fields. This solves a problem of Jarden and Narkiewicz from 2007 for quadratic number fields.

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Rational integers as sums of units -- the quadratic case

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