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arXiv · 1706.10296

Distribution of real algebraic integers

Dzianis Kaliada
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Abstract

In the paper, we study the asymptotic distribution of real algebraic integers of fixed degree as their na\"ıve height tends to infinity. For an arbitrary interval $I \subset \mathbb{R}$ and sufficiently large $Q>0$, we obtain an asymptotic formula for the number of algebraic integers $α\in I$ of fixed degree $n$ and na\"ıve height $H(α)\le Q$. In particular, we show that the real algebraic integers of degree $n$, with their height growing, tend to be distributed like the real algebraic numbers of degree $n-1$. However, we reveal two symmetric "plateaux", where the distribution of real algebraic integers statistically resembles the rational integers.

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Dzianis Kaliada. 2018-06-18. Distribution of real algebraic integers. https://arxiv.org/abs/1706.10296

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