Related papers: Einige Bemerkungen \"uber inhomogene diophantische…
We prove an easy statement about inhomogeneous approximation in metric theory of Diophantine Approximation.
In Diophantine approximation, inhomogeneous problems are linked with homogeneous ones by means of the so-called Transference Theorems. We revisit this classical topic by introducing new exponents of Diophantine approximation. We prove that…
We survey classical and recent results on exponents of Diophantine approximation. We give only a few proofs and highlight several open problems.
We introduce an inhomogeneous variant of Kaufman's measure, with applications to diophantine approximation. In particular, we make progress towards a problem related to Littlewood's conjecture.
This paper develops the metric theory of simultaneous inhomogeneous Diophantine approximation on a planar curve with respect to multiple approximating functions. Our results naturally generalize the homogeneous Lebesgue measure and Hausdor?…
The paper is mostly a survey on recent results in Diophantine approximation, with emphasis on properties of exponents measuring various notions of Diophantine <approximation.
We study some problems in metric Diophantine approximation over local fields of positive characteristic.
This paper addresses a problem recently raised by Laurent and Nogueira about inhomogeneous Diophantine approximation with coprime integers. As a corollary of our main theorem we obtain an improvement of the best known exponent of…
In this paper we develop a general theory of metric Diophantine approximation for systems of linear forms. A new notion of `weak non-planarity' of manifolds and more generally measures on the space of $m\times n$ matrices over $\Bbb R$ is…
We discuss several open problems in Diophantine approximation. Among them there are famous Littlewood's and Zaremba's conjectures as well as some new and not so famous problems.
The goal of this paper is to develop a coherent theory for inhomogeneous Diophantine approximation on curves in $R^n$ akin to the well established homogeneous theory. More specifically, the measure theoretic results obtained generalize the…
The inhomogeneous metric theory for the set of simultaneously $\psi$-approximable points lying on a planar curve is developed. Our results naturally incorporate the homogeneous Khintchine-Jarnik type theorems recently established in [Ann.…
We provide an extension of the transference results of Beresnevich and Velani connecting homogeneous and inhomogeneous Diophantine approximation on manifolds and provide bounds for inhomogeneous Diophantine exponents of affine subspaces and…
We give some comments on W.M. Schmidt's theorem on Diophantine approximations with positive integers and our recent results on the topic.
In this paper we develop a metric theory of inhomogeneous Diophantine approximation for the case of a fixed matrix. We use transference principle to connect uniform Diophantine properties of a pair $(\Theta, \pmb{\eta})$ of a matrix and a…
We study the problem of Diophantine approximation on lines in $\mathbb{R}^d$ under certain primality restrictions.
We demonstrate how connections between graph theory and Diophantine approximation can be used in conjunction to give simple and accessible proofs of seemingly difficult results in both subjects.
A basic question of Diophantine approximation, which is the first issue we discuss, is to investigate the rational approximations to a single real number. Next, we consider the algebraic or polynomial approximations to a single complex…
Recent years have seen very important developments at the interface of Diophantine approximation and homogeneous dynamics. In the first part of the paper we give a brief exposition of a dictionary developed by Dani and Kleinbock-Margulis…
We prove new results, related to the Littlewood and Mixed Littlewood conjectures in Diophantine approximation.