Zobrazeno 1 - 10
of 384
pro vyhledávání: '"37A17"'
Autor:
Pfitscher, René
On a generalized flag variety of rank one, we count rational approximations to a real point chosen randomly according to the Riemannian volume. In particular, our results apply to Grassmann varieties and quadric hypersurfaces. The proof uses exponent
Externí odkaz:
http://arxiv.org/abs/2410.16508
We prove an effective slope gap distribution result first for the square torus and then for general lattice translation surfaces. As a corollary, we obtain a dynamical proof for an effective gap distribution result for the Farey fractions. As an inte
Externí odkaz:
http://arxiv.org/abs/2409.15660
We fully describe all horocycle orbit closures in $ \mathbb{Z} $-covers of compact hyperbolic surfaces. Our results rely on a careful analysis of the efficiency of all distance minimizing geodesic rays in the cover. As a corollary we obtain in this s
Externí odkaz:
http://arxiv.org/abs/2409.10004
Autor:
Aggarwal, Gaurav, Ghosh, Anish
The famous L\'{e}vy-Khintchine theorem is a beautiful limiting law for the denominators of the convergents of the continued fraction expansion of a real number. In a recent breakthrough, Cheung and Chevallier (Annales scientifiques de l'ENS, 2024) ex
Externí odkaz:
http://arxiv.org/abs/2408.15683
Autor:
Zheng, Cheng
We give a simple proof about the topological rigidity of closures of certain sparse unipotent orbits in $G/\Gamma$ where $G=\prod_{i=1}^k\operatorname{SL}_2(\mathbb R)$ and $\Gamma$ is an irreducible lattice in $G$.
Comment: 18 pages
Comment: 18 pages
Externí odkaz:
http://arxiv.org/abs/2408.13861
Autor:
Chow, Michael, Sarkar, Pratyush
Let $\Gamma$ be a Zariski dense $\Theta$-Anosov subgroup of a connected semisimple real algebraic group for some nonempty subset of simple roots $\Theta$. In the Anosov setting, there is a natural compact metric space $\mathcal{X}$ equipped with a fa
Externí odkaz:
http://arxiv.org/abs/2408.11274
We extend Ratner's theorem on equidistribution of individual orbits of unipotent flows on finite volume homogeneous spaces of Lie groups to trajectories of non-contracting curves definable in polynomially bounded o-minimal structures. To be precise,
Externí odkaz:
http://arxiv.org/abs/2407.04935
Autor:
Aggarwal, Gaurav, Ghosh, Anish
We study non-expanding random walks on the space of affine lattices and establish a new classification theorem for stationary measures. Further, we prove a theorem that relates the genericity with respect to these random walks to Birkhoff genericity.
Externí odkaz:
http://arxiv.org/abs/2406.15824
Autor:
Lin, Zuo
We prove an effective density theorem with polynomial error rate for orbits of upper triangular subgroup of $\mathrm{SL}_2(\mathbb{Q}_p)$ in $\mathrm{SL}_2(\mathbb{Q}_p) \times \mathrm{SL}_2(\mathbb{Q}_p)$ for prime number $p > 3$. The proof is based
Externí odkaz:
http://arxiv.org/abs/2404.13931
Autor:
Cheung, Yitwah, Quas, Anthony
The BCZ map was introduced in 2001 by Boca, Cobeli and Zaharescu as a tool to study the statistical properties of Farey sequences, whose relation to Riemann Hypothesis dates back to Franel and Landau. Later, J. Athreya and the first author observed t
Externí odkaz:
http://arxiv.org/abs/2403.14976