# On distribution of points with conjugate algebraic integer coordinates close to planar curves

@inproceedings{VBernik2017OnDO, title={On distribution of points with conjugate algebraic integer coordinates close to planar curves}, author={V.Bernik and F.Gotze and A.Gusakova}, year={2017} }

Let φ : R → R be a continuously differentiable function on an interval J ⊂ R and let α = (α1, α2) be a point with algebraic conjugate integer coordinates of degree ≤ n and of height ≤ Q. Denote by M̃ φ (Q, γ, J) the set of points α such that |φ(α1) − α2| ≤ c1Q −γ . In this paper we show that for a real 0 < γ < 1 and any sufficiently large Q there exist positive values c2 < c3, which are independent of Q, such that c2 ·Q n−γ < #M̃ φ (Q, γ, J) < c3 ·Q n−γ .

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