Effective joint equidistribution of primitive rational points on expanding horospheres. (English) Zbl 1525.37005
An effective version of a result due to M. Einsiedler et al. [Compos. Math. 152, No. 4, 667–692 (2016; Zbl 1382.37032)] is found, giving a rate of equidistribution of primitive rational points on expanding horospheres in the space of unimodular lattices in dimensions greater than two. The approach uses spectral theory and bounds for Kloosterman sums rather than techniques from homogeneous dynamics that do not give effective rates. As an application a rate of convergence to the limiting distribution for suitably rescaled diameters of random circulant graphs is found.
Reviewer: Thomas B. Ward (Durham)
MSC:
| 37A44 | Relations between ergodic theory and number theory |
| 37A46 | Relations between ergodic theory and harmonic analysis |
| 37A17 | Homogeneous flows |
| 11L05 | Gauss and Kloosterman sums; generalizations |
Citations:
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