Israel Journal of Mathematics

, Volume 176, Issue 1, pp 419–444

Strong wavefront lemma and counting lattice points in sectors

Article

DOI: 10.1007/s11856-010-0035-8

Cite this article as:
Gorodnik, A., Oh, H. & Shah, N. Isr. J. Math. (2010) 176: 419. doi:10.1007/s11856-010-0035-8

Abstract

We compute the asymptotics of the number of integral quadratic forms with prescribed orthogonal decompositions and more generally, the asymptotics of the number of lattice points lying in sectors of affine symmetric spaces. A new key ingredient in this article is the strong wavefront lemma, which shows that the generalized Cartan decomposition associated to a symmetric space is uniformly Lipschitz.

Copyright information

© Hebrew University Magnes Press 2010

Authors and Affiliations

  1. 1.School of MathematicsUniversity of BristolBristolUK
  2. 2.Math DepartmentBrown UniversityProvidenceUSA
  3. 3.School of MathematicsTIFRMumbaiIndia