Related papers: Metric Diophantine approximation over a local fiel…

We prove a strengthened version of the inhomogeneous Sprindzhuk conjecture in metric Diophantine approximation, over a local field of positive characteristic. The main tool is the transference principle of Beresnevich and Velani coupled…

We study some problems in metric Diophantine approximation over local fields of positive characteristic.

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 positive characteristic versions of the logarithm laws of Sullivan and Kleinbock-Margulis and obtain related results in Metric Diophantine Approximation.

We give an elementary proof of a recent metrical Diophantine result by D. Kleinbock related to badly approximable vectors in affine subspaces.

In this paper we present a new approach to prove effective results in Diophantine approximation. We then use it to prove an effective theorem on the simultaneous approximation of two algebraic numbers satisfying an algebraic equation with…

There are abundant results on Diophantine approximation over fields of positive characteristic (see the survey papers [13, 25]), but there is very little information about simultaneous approximation. In this paper, we develop a technique of…

We place the theory of metric Diophantine approximation on manifolds into a broader context of studying Diophantine properties of points generic with respect to certain measures on $\Bbb R^n$. The correspondence between multidimensional…

We study the problem of improving Dirichlet's theorem of metric Diophantine approximation in the $S$-adic setting. Our approach is based on translation of the problem related to Dirichlet improvability into a dynamical one, and the main…

We establish the convergence theory of multiplicative Diophantine approximation for all non-degenerate, smooth manifolds. We also settle said convergence theory for all affine subspaces satisfying a highly generic and essentially optimal…

In a landmark paper, D.Y. Kleinbock and G.A. Margulis established the fundamental Baker-Sprindzuk conjecture on homogeneous Diophantine approximation on manifolds. Subsequently, there has been dramatic progress in this area of research.…

We prove a quantitative theorem for Diophantine approximation by rational points on spheres. Our results are valid for arbitrary unimodular lattices and we further prove 'spiraling' results for the direction of approximates. These results…

The goal of this paper is to establish a complete Khintchine-Groshev type theorem in both homogeneous and inhomogeneous setting, on analytic nondegenerate manifolds over a local field of positive characteristic. The dual form of Diophantine…

In these notes, we begin by recalling aspects of the classical theory of metric Diophantine approximation; such as theorems of Khintchine, Jarn\'{\i}k, Duffin-Schaeffer and Gallagher. We then describe recent strengthening of various…

We develop the metric theory of Diophantine approximation on homogeneous varieties of semisimple algebraic groups and prove results analogous to the classical Khinchin and Jarnik theorems. In full generality our results establish…

Diophantine approximation is traditionally the study of how well real numbers are approximated by rationals. We propose a model for studying Diophantine approximation in an arbitrary totally bounded metric space where the rationals are…

This paper deals with a method for the approximation of a spectral density function among the solutions of a generalized moment problem a` la Byrnes/Georgiou/Lindquist. The approximation is pursued with respect to the Kullback-Leibler…

We extend the key formula which intertwines multiplicative Markoff-Lagrange spectrum and symbolic dynamics. The proof uses complex analysis and elucidates the strategy of the problem. Moreover, the new method applies to a wide variety of…

This paper goes back to a famous problem of Mahler in metrical Diophantine approximation. The problem has been settled by Sprindzuk and subsequently improved by Alan Baker and Vasili Bernik. In particular, Bernik's result establishes a…

We study the Diophantine transference principle over function fields. By adapting the approach of Beresnevich and Velani to the function field set-up, we extend many results from homogeneous Diophantine approximation to the realm of…