Counting Algebraic Integers of Bounded Height in Cyclotomic Fields

Phillip Harris; John Yin

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arXiv · 2606.15374

Counting Algebraic Integers of Bounded Height in Cyclotomic Fields

Phillip Harris·John Yin

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Abstract

In this note, we fix a height bound $B$, and give a bound on the number of algebraic integers and units of absolute height at most $B$ in cyclotomic extensions $\mathbb{Q}[\zeta_q]$, where $q$ is a prime power. The bound is asymptotic in $q$.

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Phillip Harris, John Yin. 2026-06-13. Counting Algebraic Integers of Bounded Height in Cyclotomic Fields. https://arxiv.org/abs/2606.15374

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