Hyperbolic lattice point problems
نویسندگان
چکیده
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...
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be the set of all non-negative integer combinations of a1, . . . , ad, or, in other words, the semigroup S ⊂ Z+ of non-negative integers generated by a1, . . . , ad. What does S look like? In particular, what is the largest integer not in S? (It is well known and easy to see that all sufficiently large integers are in S.) How many positive integers are not in S? How many positive integers withi...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2011
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-2010-10536-1