2017/06/30 by Kaliada, Dzianis
#11K38 (Secondary) #11N45 (Primary) #11R04 #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.1706.10296
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 ⊂ ℝ and sufficiently large Q>0, we obtain an asymptotic formula for the number of algebraic integers α∈ I of fixed degree n and na"ıve 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.