منابع مشابه
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...
متن کاملOn the Distribution of Lattice Points in Thin Annuli
We show that the number of lattice points lying in a thin annulus has a Gaussian value distribution if the width of the annulus tends to zero sufficiently slowly as we increase the inner radius.
متن کاملCritical Dimensions for counting Lattice Points in Euclidean Annuli
We study the number of lattice points in R, d ≥ 2, lying inside an annulus as a function of the centre of the annulus. The average number of lattice points there equals the volume of the annulus, and we study the L1 and L2 norms of the remainder. We say that a dimension is critical, if these norms do not have upper and lower bounds of the same order as the radius goes to infinity. In [6], it wa...
متن کاملLattice point counting and harmonic analysis
We explain the application of harmonic analysis to count lattice points in large regions. We also present some of our recent results in the three-dimensional case.
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ژورنال
عنوان ژورنال: The Journal of Geometric Analysis
سال: 2020
ISSN: 1050-6926,1559-002X
DOI: 10.1007/s12220-020-00568-y