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G. I. Arkhipov, V. N. Chubarikov

Asymptotic formula for the number of points of a lattice in the circle on the Lobachevsky plane

We define the distance d(z, z′) between points z = x + iy and z′ = x′ + iy′ in the upper half-plane, setting

where u = |z – z′|²/(yy′). The circle K(z₀, T) with centre in a point z₀ consists of the points z satisfying the inequality d(z, z₀) ≤ T. Let N(z₀, T) be the number of elements γ of the modular group PSL₂(Z) such that the point yz₀ lies in the circle K(z₀, T). In this paper, we refine the remainder term in the asymptotic formula for N(z₀, T).

Discrete Mathematics and Applications, Walter de Gruyter

Print ISSN: 0924-9266
Volume: 16, 09/2006
Pages: 461 - 469

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