Logarithm laws for one parameter unipotent flows

Dubi Kelmer; Amir Mohammadi

Logarithm laws for one parameter unipotent flows

Dynamical Systems 2016-10-03 v3 Number Theory

Authors: Dubi Kelmer , Amir Mohammadi

Abstract

We prove logarithm laws and shrinking target properties for unipotent flows on the homogenous space $\Gamma\bs G$ with $G=\SL_2(\bbR)^{r_1}\times\SL_2(\bbC)^{r_2}$ and $\Gamma\subseteq G$ an irreducible non-uniform lattice. Our method relies on certain estimates for the norms of (incomplete) theta series in this setting.

Keywords

geodesic flow limit theorems gamma-convergence and homogenization

Cite

@article{arxiv.1105.5325,
  title  = {Logarithm laws for one parameter unipotent flows},
  author = {Dubi Kelmer and Amir Mohammadi},
  journal= {arXiv preprint arXiv:1105.5325},
  year   = {2016}
}

Comments

This version corrects a mistake appearing in previous versions of this paper. Explicitly, Lemma 2.8 in the previous version is false as stated, and consequently so is the proof of Lemma 2.9 and Theorem 3. In this version we removed the false statement and proved a modified version of Lemma 2.8 which is sufficient for the proof of Theorem 3

Logarithm laws for one parameter unipotent flows

Abstract

Keywords

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