Abstract
In the paper, we study the asymptotic distribution of real algebraic integers of fixed degree as their naïve height tends to infinity. For an arbitrary interval I⊂R and sufficiently large Q>0, we obtain an asymptotic formula for the number of algebraic integers α∈I of fixed degree n and naïve height H(α)≤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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