Lattice points on hyperboloids of one sheet

被引:0
作者
Baragar, Arthur [1 ]
机构
[1] Univ Nevada, Dept Math Sci, Las Vegas, NV 89154 USA
来源
NEW YORK JOURNAL OF MATHEMATICS | 2014年 / 20卷
关键词
Gauss' circle problem; lattice points; orbits; Hausdorff dimension; ample cone; KLEINIAN-GROUPS; K3; SURFACES; LIMIT-SETS; SPACE;
D O I
暂无
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
The problem of counting lattice points on a hyperboloid of two sheets is Gauss' circle problem in hyperbolic geometry. The problem of counting lattice points on a hyperboloid of one sheet does not have the same geometric interpretation, and in general, the solution(s) to Gauss' circle problem gives a lower bound, but not an upper bound. In this paper, we describe an exception. Given an ample height, and a lattice on a hyperboloid of one sheet generated by a point in the interior of the effective cone, the problem can be reduced to Gauss' circle problem.
引用
收藏
页码:1253 / 1268
页数:16
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