Related papers: An inequality for Diophantine exponents in the cas…
We obtain some new inequalities between the ordinary and the uniform Diophantine exponents for simultaneous Diophantine approximation to four real numbers.
We find new inequalities between uniform and individual Diophantine exponents for three-dimensional Diophantine approximations. Also we give a result for two linear forms in two variables. The results improves V.Jarnik's theorem (1954).
We aim to fill a gap in the proof of an inequality relating two exponents of uniform Diophantine approximation stated in a paper by Bugeaud. We succeed to verify the inequality in several instances, in particular for small dimension.…
In this paper we prove transference inequalities for regular and uniform Diophantine exponents in the weighted setting. Our results generalize the corresponding inequalities that exist in the `non-weighted' case.
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…
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 survey classical and recent results on exponents of Diophantine approximation. We give only a few proofs and highlight several open problems.
We provide a lower bound for the ratio between the ordinary and uniform exponent of both simultaneous Diophantine approximation and Diophantine approximation by linear forms in any dimension. This lower bound was conjectured by Schmidt and…
We study properties of Diophantine exponents of lattices and so-called related "weak" uniform approximations introduced in recent papers by Oleg German, in the simplest two-dimensional case. In contrast to the multidimensional case, in the…
We discuss the problem of finding optimal exponents in Diophantine estimates involving one real number and, in some cases where such an exponent is known, present some properties of the corresponding extremal numbers.
The paper is mostly a survey on recent results in Diophantine approximation, with emphasis on properties of exponents measuring various notions of Diophantine <approximation.
In this paper we study the spectrum of weak uniform Diophantine exponents of lattices and obtain its complete description in the two-dimensional case.
In this paper we give a simple proof of an inequality for intermediate Diophantine exponents obtained recently by W. M. Schmidt and L. Summerer.
In this paper we improve estimates of Jarnik and Apfelbeck for uniform Diophantine exponents of transposed systems of linear forms and generalize to the case of an arbitrary system the estimates of Laurent and Bugeaud for individual…
We prove a strong simultaneous Diophantine approximation theorem for values of additive and multiplicative functions provided that the functions have certain regularity on the primes.
We prove a new lower bound for the exponent of growth of the best two-dimensional Diophantine approximations with respect to Euclidean norm.
In the present paper, we have developed a method for solving \textit{diophantine inequalities} using their relationship with the \textit{difference between consecutive primes}. Using this approach we have been able to prove some theorems,…
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…
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…
In this paper we prove that uniform Diophantine exponents of lattices attain only trivial values.