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- Title
Asymptotic formula for the number of points of a lattice in the circle on the Lobachevsky plane.
- Authors
Arkhipov, G. I.; Chubarikov, V. N.
- Abstract
We define the distance d(z, z′) between points z = x + iy and z′ = x′ + iy′ in the upper half-plane, setting d = ln(u + 2 + √u2 + 4u/2), 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).
- Subjects
DISTANCES; CIRCLE; MATHEMATICAL inequalities; HYPERBOLIC geometry; LATTICE theory; MODULAR groups
- Publication
Discrete Mathematics & Applications, 2006, Vol 16, Issue 5, p461
- ISSN
0924-9265
- Publication type
Article
- DOI
10.1515/156939206779238445