Related papers: Exponents of Diophantine approximation
We study metric Diophantine approximation in local fields of positive characteristic. Specifically, we study the problem of improving Dirichlet's theorem in Diophantine approximation and prove very general results in this context.
We prove a number of results on the metric and non-metric theory of Diophantine approximation for Yu's multidimensional variant of Mahler's classification of transcendental numbers. Our results arise as applications of well known results in…
We formulate an exponential Diophantine equation, which is is some sense one order higher that Fermat's Last Theorem. We also give three examples of solutions to this exponential Diophantine equation and formulate a conjecture.
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 prove inequalities for multiplicative analogues of Diophantine exponents, similar to the ones known in the classical case. Particularly, we show that a matrix is badly approximable if and only if its transpose is badly…
We consider the problem of Diophantine approximation on semisimple algebraic groups by rational points with restricted numerators and denominators and establish a quantitative approximation result for all real points in the group by…
We obtain some new inequalities between the ordinary and the uniform Diophantine exponents for simultaneous Diophantine approximation to four real numbers.
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.
We prove a new quantitative result on the degeneracy of the dimension of the subspace spanned by the best Diophantine approximations for a linear form.
We study the problem of Diophantine approximation on lines in $\mathbb{R}^d$ under certain primality restrictions.
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…
The objective of this paper is to (partially) address the issue of finding an analogue to Khintchine's theorem for IFS Fractals. We study the convergence case for Diophantine approximations, and show an improved result for higher…
We study the problem of Diophantine approximation on lines in R^2 with prime numerator and denominator.
A paradigm for a global algebraic number theory of the reals is formulated with the purpose of providing a unified setting for algebraic and transcendental number theory. This is achieved through the study of subgroups of nonstandard models…
The goal of this survey is to discuss the Quantitative non-Divergence estimate on the space of lattices and present a selection of its applications. The topics covered include extremal manifolds, Khintchine-Groshev type theorems, rational…
We describe the spectrum of ordinary Diophantine exponents for $d$-dimensional lattices. The result reduces the problem to two-dimensional case and uses argument of metric theory.
This text is a slightly expanded version of a survey article on certain aspects of low dimensional dynamics and number theory written after a kind invitation by the editors of the Notices of the American Mathematical Society.
I present here the proofs of results, which are obtained in my papers "On the linear forms with algebraic coefficoients of logarithms of algebraic numbers", VINITI, 1996, 1617-B96, pp. 1 - 23 (in Russian), and "On the systems of linear…
We prove a new lower bound for the exponent of growth of the best two-dimensional Diophantine approximations with respect to Euclidean norm.
We give an elementary proof of a recent metrical Diophantine result by D. Kleinbock related to badly approximable vectors in affine subspaces.