A lattice point problem in hyperbolic space.

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The Variance of the Hyperbolic Lattice Point Counting Function

The problem of estimating the number of points of a lattice that lie in a ball, is often called the circle problem. In the case of lattices in Euclidean space, this question goes back at least as far as Gauss. If we call Nρ the number of points of Z inside the ball B(0, ρ), then one easily sees that the leading term of Nρ is the area, πρ, of B(0, ρ). It is not difficult to show that the error t...

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ژورنال

عنوان ژورنال: Michigan Mathematical Journal

سال: 1983

ISSN: 0026-2285

DOI: 10.1307/mmj/1029002905