 

Arthur Baragar
Lattice points on hyperboloids of one sheet view print


Published: 
December 12, 2014

Keywords: 
Gauss' circle problem, lattice points, orbits, Hausdorff dimension, ample cone 
Subject: 
11D45, 11P21, 20H10, 22E40, 11N45, 14J28, 11G50, 11H06 


Abstract
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.


Acknowledgements
This work is based upon research supported by the National Security Agency under grant H982300810022.


Author information
Department of Mathematical Sciences, University of Nevada, Las Vegas, NV 891544020
baragar@unlv.nevada.edu

