Loading...
Please wait, while we are loading the content...
Similar Documents
Lifting, restricting and sifting integral points on affine homogeneous varieties
| Content Provider | Scilit |
|---|---|
| Author | Gorodnik, Alexander Nevo, Amos |
| Copyright Year | 2012 |
| Description | Journal: Compositio Mathematica In [Gorodnik and Nevo,Counting lattice points, J. Reine Angew. Math.663(2012), 127–176] an effective solution of the lattice point counting problem in general domains in semisimpleS-algebraic groups and affine symmetric varieties was established. The method relies on the mean ergodic theorem for the action ofGonG/Γ, and implies uniformity in counting over families of lattice subgroups admitting a uniform spectral gap. In the present paper we extend some methods developed in [Nevo and Sarnak,Prime and almost prime integral points on principal homogeneous spaces, Acta Math.205(2010), 361–402] and use them to establish several useful consequences of this property, including: (1)effective upper bounds on lifting for solutions of congruences in affine homogeneous varieties; (2)effective upper bounds on the number of integral points on general subvarieties of semisimple group varieties; (3)effective lower bounds on the number of almost prime points on symmetric varieties; (4)effective upper bounds on almost prime solutions of congruences in homogeneous varieties. |
| Ending Page | 1716 |
| Starting Page | 1695 |
| ISSN | 00221295 |
| e-ISSN | 15705846 |
| DOI | 10.1112/s0010437x12000516 |
| Journal | Compositio Mathematica |
| Issue Number | 6 |
| Volume Number | 148 |
| Language | English |
| Publisher | Wiley-Blackwell |
| Publisher Date | 2012-10-11 |
| Access Restriction | Open |
| Subject Keyword | Journal: Compositio Mathematica Applied Mathematics Homogeneous Varieties Affine Homogeneous Sifting Integral Integral Points |
| Content Type | Text |
| Resource Type | Article |
| Subject | Algebra and Number Theory |
