Distribution of algebraic integers of a given degree in the real line
In the article, we have obtained an asymptotic formula for the number of algebraic integers a of an arbitrary given degree n that have the height H(a) ≤ Q and lie in the interval I, as Q tends to infninity. We have proved that the error term in this formula is of the order O(Q n-1) for infinitely many intervals. We have shown that algebraic integers of the given degree n are distributed asymptotically just like algebraic numbers of the degree n - 1.