Zobrazeno 1 - 10
of 23
pro vyhledávání: '"Nesharim, Erez"'
In 1998 Kleinbock conjectured that any set of weighted badly approximable $d\times n$ real matrices is a winning subset in the sense of Schmidt's game. In this paper we prove this conjecture in full for vectors in $\mathbf{R}^d$ in arbitrary dimensio
Externí odkaz:
http://arxiv.org/abs/2005.11947
In this paper we prove that badly approximable points on any analytic non-degenerate curve in $\mathbb{R}^n$ is an absolute winning set. This confirms a key conjecture in the area stated by Badziahin and Velani (2014) which represents a far-reaching
Externí odkaz:
http://arxiv.org/abs/2005.02128
Publikováno v:
Mathematika, 67, (2021), 196-213
We consider Schmidt's game on the space of compact subsets of a given metric space equipped with the Hausdorff metric, and the space of continuous functions equipped with the supremum norm. We are interested in determining the generic behaviour of ob
Externí odkaz:
http://arxiv.org/abs/1907.07394
We prove a version of the Khinchine--Groshev theorem for Diophantine approximation of matrices subject to a congruence condition. The proof relies on an extension of the Dani correspondence to the quotient by a congruence subgroup. This correspondenc
Externí odkaz:
http://arxiv.org/abs/1902.01381
The $p$-adic Littlewood Conjecture due to De Mathan and Teuli\'e asserts that for any prime number $p$ and any real number $\alpha$, the equation $$\inf_{|m|\ge 1} |m|\cdot |m|_p\cdot |\langle m\alpha \rangle|\, =\, 0 $$ holds. Here, $|m|$ is the usu
Externí odkaz:
http://arxiv.org/abs/1806.04478
Schmidt games and the Cantor winning property give alternative notions of largeness, similar to the more standard notions of measure and category. Being intuitive, flexible, and applicable to recent research made them an active object of study. We su
Externí odkaz:
http://arxiv.org/abs/1804.06499
This paper deals with the analogue of Inhomogeneous Diophantine Approximation in function fields. The inhomogeneous approximation constant of a Laurent series $\theta\in\mathbb F_q\left(\left(\frac{1}{t}\right)\right)$ with respect to $\gamma\in\math
Externí odkaz:
http://arxiv.org/abs/1512.07231
Autor:
Nesharim, Erez, Simmons, David S.
Publikováno v:
Acta Arith. 164 (2014), no. 2, 145--152
J. An (2013) proved that for any $s,t \geq 0$ such that $s + t = 1$, $\mathbf{Bad}(s,t)$ is $(34\sqrt 2)^{-1}$-winning for Schmidt's game. We show that using the main lemma from An's paper one can derive a stronger result, namely that $\mathbf{Bad}(s
Externí odkaz:
http://arxiv.org/abs/1307.5037
Autor:
Nesharim, Erez
For $i, j > 0, i + j = 1$, the set of badly approximable vectors with weight $(i, j)$ is defined by $Bad(i, j) = \{(x, y) \in \R^2 : \exists c > 0 \forall q\in\N, \;\; \max\{q||qx||^{1/i}, q||qy||^{1/j} \} > c\}$, where $||x||$ is the distance of $x$
Externí odkaz:
http://arxiv.org/abs/1204.0110
Publikováno v:
Duke Mathematical Journal. 171
In this paper we prove that badly approximable points on any analytic non-degenerate curve in $\mathbb{R}^n$ is an absolute winning set. This confirms a key conjecture in the area stated by Badziahin and Velani (2014) which represents a far-reaching
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6cb6b6644a4ab9eb67d00f7a216f2357
https://doi.org/10.1215/00127094-2022-0038
https://doi.org/10.1215/00127094-2022-0038
