DISTRIBUTION OF ALGEBRAIC INTEGERS OF A GIVEN DEGREE IN THE REAL LINE
Abstract
In the article, we have obtained an asymptotic formula for the number of algebraic integers α of an arbitrary given degree n that have the height H(α) ≤ 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(Qn–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.
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