Zobrazeno 1 - 10
of 417
pro vyhledávání: '"11k60"'
Autor:
Kim, Seongmin
The Khintchine-Groshev theorem in Diophantine approximation theory says that there is a dichotomy of the Lebesgue measure of sets of $\psi$-approximable numbers, given a monotonic function $\psi$. Allen and Ram\'irez removed the monotonicity conditio
Externí odkaz:
http://arxiv.org/abs/2411.07932
Let $\{a_n\}_{n\in\mathbb{N}}$, $\{b_n\}_{n\in \mathbb{N}}$ be two infinite subsets of positive integers and $\psi:\mathbb{N}\to \mathbb{R}_{>0}$ be a positive function. We completely determine the Hausdorff dimensions of the set of all points $(x,y)
Externí odkaz:
http://arxiv.org/abs/2409.18635
Autor:
Hauke, Manuel, Ramirez, Felipe A.
We prove the inhomogeneous generalization of the Duffin-Schaeffer conjecture in dimension $m \geq 3$. That is, given $\mathbf{y}\in \mathbb{R}^m$ and $\psi:\mathbb{N}\to\mathbb{R}_{\geq 0}$ such that $\sum (\varphi(q)\psi(q)/q)^m = \infty$, we show t
Externí odkaz:
http://arxiv.org/abs/2407.05344
Autor:
Srivastava, Rajula
In this manuscript, we initiate the study of the number of rational points with bounded denominators, contained in a non-isotropic $\delta_1\times\ldots\times \delta_R$ neighborhood of a compact submanifold $\mathcal{M}$ of codimension $R$ in $\mathb
Externí odkaz:
http://arxiv.org/abs/2407.03078
The most versatile version of the classical divergence Borel-Cantelli lemma shows that for any divergent sequence of events $E_n$ in a probability space satisfying a quasi-independence condition, its corresponding limsup set $E_\infty$ has positive p
Externí odkaz:
http://arxiv.org/abs/2406.19198
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:
Ramirez, Felipe A.
In metric Diophantine approximation, one frequently encounters the problem of showing that a limsup set has positive or full measure. Often it is a set of points in $m$-dimensional Euclidean space, or a set of $n$-by-$m$ systems of linear forms, sati
Externí odkaz:
http://arxiv.org/abs/2405.03811
Autor:
Frühwirth, Lorenz, Hauke, Manuel
Given a monotonically decreasing $\psi: \mathbb{N} \to [0,\infty)$, Khintchine's Theorem provides an efficient tool to decide whether, for almost every $\alpha \in \mathbb{R}$, there are infinitely many $(p,q) \in \mathbb{Z}^2$ such that $\left\lvert
Externí odkaz:
http://arxiv.org/abs/2403.11257
Autor:
Arenas-Carmona, Luis, Bravo, Claudio
We use the theory of arithmetic quotients of the Bruhat-Tits tree developed by Serre and others to obtain Dirichlet-style theorems for Diophantine approximation on global function fields. This approach allows us to find sharp values for the constants
Externí odkaz:
http://arxiv.org/abs/2401.05169
Autor:
Marklof, Jens
This paper studies the logarithmic moments of the smallest denominator of all rationals in a shrinking interval with random center. Convergence follows from the more general results in [arXiv:2310.11251, Bull. Lond. Math. Soc., to appear], and the ke
Externí odkaz:
http://arxiv.org/abs/2312.15303