The quantitative behaviour of polynomial orbits on nilmanifolds

@article{Green2007TheQB,
  title={The quantitative behaviour of polynomial orbits on nilmanifolds},
  author={B. Green and T. Tao},
  journal={arXiv: Number Theory},
  year={2007}
}
A theorem of Leibman asserts that a polynomial orbit $(g(1),g(2),g(3),\ldots)$ on a nilmanifold $G/\Gamma$ is always equidistributed in a union of closed sub-nilmanifolds of $G/\Gamma$. In this paper we give a quantitative version of Leibman's result, describing the uniform distribution properties of a finite polynomial orbit $(g(1),\ldots,g(N))$ in a nilmanifold. More specifically we show that there is a factorization $g = \epsilon g'\gamma$, where $\epsilon(n)$ is "smooth", $\gamma(n)$ is… Expand

Figures from this paper

Higher order almost automorphy, recurrence sets and the regionally proximal relation
Sarnak's Conjecture for nilsequences on arbitrary number fields and applications.
Convergence Results for Systems of Linear Forms on Cyclic Groups and Periodic Nilsequences
Probabilistic nilpotence in infinite groups
Equidistribution of sparse sequences on nilmanifolds
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 59 REFERENCES
The Mobius function is strongly orthogonal to nilsequences
AN INVERSE THEOREM FOR THE GOWERS $U^3(G)$ NORM
  • B. Green, T. Tao
  • Mathematics
  • Proceedings of the Edinburgh Mathematical Society
  • 2008
Spectra of nilflows
Universal characteristic factors and Furstenberg averages
AN INVERSE THEOREM FOR THE GOWERS U4-NORM
Ratner's Theorems on Unipotent Flows
Linear equations in primes
...
1
2
3
4
5
...