Zobrazeno 1 - 10
of 210
pro vyhledávání: '"Ghosh, Anish"'
Autor:
Aggarwal, Gaurav, Ghosh, Anish
We prove a sharp upper bound on the Hausdorff dimension of weighted singular vectors in $\mathbb{R}^m$ using dynamics on homogeneous spaces, specifically the method of integral inequalities. Together with the lower bound proved recently by Kim and Pa
Externí odkaz:
http://arxiv.org/abs/2410.09742
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:
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:
Aggarwal, Gaurav, Ghosh, Anish
In this paper, we consider the problem of counting Diophantine inequalities with multiple natural constraints. We prove a very general result in this setting using dynamical techniques. More precisely, we consider the joint asymptotic distribution of
Externí odkaz:
http://arxiv.org/abs/2401.02747
In this paper we investigate the shrinking target property for irrational rotations. This was first studied by Kurzweil (1951) and has received considerable interest of late. Using a new approach, we generalize results of Kim (2007) and Shapira (2013
Externí odkaz:
http://arxiv.org/abs/2307.10122
In this paper we develop a general framework of badly approximable points in a metric space $X$ equipped with a $\sigma$-finite doubling Borel regular measure $\mu$. We establish that under mild assumptions the $\mu$-measure of the set of badly appro
Externí odkaz:
http://arxiv.org/abs/2307.10109
Autor:
Aggarwal, Gaurav, Ghosh, Anish
We prove central limit theorems for Diophantine approximations with congruence conditions and for inhomogeneous Diophantine approximations following the approach of Bj\"{o}rklund and Gorodnik. The main tools are the cumulant method and dynamics on ho
Externí odkaz:
http://arxiv.org/abs/2306.02304
Publikováno v:
Journal f\"ur die reine und angewandte Mathematik (Crelles Journal), vol. 2024, no. 815, 2024, pp. 71-106
In this paper we prove a conjecture of Kleinbock and Tomanov \cite[Conjecture~FP]{KT} on Diophantine properties of a large class of fractal measures on $\mathbb{Q}_p^n$. More generally, we establish the $p$-adic analogues of the influential results o
Externí odkaz:
http://arxiv.org/abs/2209.10456
We prove that for any proper metric space $X$ and a function $\psi:(0,\infty)\to(0,\infty)$ from a suitable class of approximation functions, the Hausdorff dimensions of the set $W_\psi(Q)$ of all points $\psi$-well-approximable by a well-distributed
Externí odkaz:
http://arxiv.org/abs/2208.14204
Autor:
Ghosh, Anish, Kumaraswamy, V. Vinay
Publikováno v:
IMRN, Vol. 2023, Issue 13, pp. 11471-11498
In this article we establish two new results on quantitative Diophantine approximation for one-parameter families of diagonal ternary indefinite forms. In the first result, we consider quadratic forms taking values at prime points. In the second, we
Externí odkaz:
http://arxiv.org/abs/2111.12069