### Far Eastern Mathematical Journal

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On the distribution of real algebraic numbers of equal height

Koleda D.V.

2018, issue 1, Ñ. 56-70

Abstract
In the paper we find the asymptotic number of algebraic numbers of fixed degree $n\ge 1$ and height H lying in an interval $I\subseteq\mathbb{R}$ as $H\to\infty$.

Keywords:
algebraic numbers, distribution of algebraic numbers, integer polynomials, generalized Farey sequences

#### References

[1] S.-J. Chern, J.D. Vaaler, “The distribution of values of Mahler’s measure”, J. Reine Angew. Math., 540, (2001), 1–47.
[2] D. Masser, J.D. Vaaler, “Counting algebraic numbers with large height I”, Diophantine Approximation, Dev. Math., 16, Springer, Vienna, 2008, 237–243.
[3] D. Masser, J.D. Vaaler, “Counting algebraic numbers with large height. II”, Trans. Amer. Math. Soc., 359:1, (2007), 427–445.
[4] R. Grizzard, J. Gunther, “Slicing the stars: counting algebraic numbers, integers, and units by degree and height”, Algebra Number Theory, 11:6, (2017), 1385–1436.
[5] H. Brown, K. Mahler, “A generalization of Farey sequences: Some exploration via the computer”, J. Number Theory, 3:3, (1971), 364–370.