相关论文: A simple proof of Schmidt-Summerer's inequality

We give a simplified exposition of the easiest case of a breakthrough result by D.Badziahin, A.Pollington and S.Velani related to W.M.Schmidt's conjecture.

We prove a Diophantine approximation inequality for closed subschemes on surfaces which can be viewed as a joint generalization of recent inequalities of Ru-Vojta and Heier-Levin in this context. As applications, we study various…

This paper uses W. M. Schmidt's idea formulated in 1967 to generalise the classical theory of Diophantine approximation to subspaces of $\mathbb{R}^n$. Given two subspaces of $\mathbb{R}^n$ $A$ and $B$ of respective dimensions $d$ and $e$…

The present paper analyzes the discrepancy of distribution of rational points on general semisimple algebraic group varieties. The results include mean-square, almost sure, and uniform discrepancy estimates with explicit error bounds, which…

In the paper we prove a new upper bound for Heilbronn's exponential sum and obtain some applications of our result to distribution of Fermat quotients.

In this paper we shall prove a sharpened version of the Finsler-Hadwiger inequality which is a strong generalization of Weitzenbock inequality. After that we give another refinement of this inequality and in the final part we provide some…

We prove new results, related to the Littlewood and Mixed Littlewood conjectures in 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, an inequality of Simpson type for quasi-convex mappings are proved. The constant in the classical Simpson's inequality is improved. Furthermore, the obtained bounds can be (much) better than some recently obtained bounds.…

In this note we prove an inequality for t-geometric means that immediately implies the recent results of Audenaert [2] and Hayajneh-Kittaneh [6].

In the current note, we present a new, short proof of the famous AM-GM-HM inequality using only induction and basic calculus.

The purpose of this paper is to provide a random version of Simons' inequality.

In this paper we prove an existence theorem concerning linear forms of a given Diophantine type and apply it to study the structure of the spectrum of lattice exponents.

We give a simpler proof of a result of Holland concerning a mixed arithmetic-geometric mean inequality. We also prove a result of mixed mean inequality involving the symmetric means.

We give a simple proof of the existence of a minimizer for the Sobolev inequality. Our proof is based on a representation formula via a cut-off fundamental solution.

We prove the following superexponential distribution inequality: for any integrable $g$ on $[0,1)^{d}$ with zero average, and any $\lambda>0$ \[ |\{ x \in [0,1)^{d} \; :\; g \geq\lambda \}| \leq e^{-…

This short and simple communication is motivated by recent papers by L. Colzani and A. Kochergin. We give a brief analysis of an example by Poincar\'{e} related to sums of the type $ \sum_{k=0}^{t-1} f(k{\alpha}+{x})$ where $f$ is a…

In this paper we aim to prove two inequalities involving the classical approximation constants $w_{n}^{\prime}(\zeta),\hat{w}_{n}^{\prime}(\zeta)$ that stem from the simultaneous approximation problem $|\zeta^{j}x-y_{j}|$, $1\leq j\leq n$,…

In this note, we present an improvement to a recent result due to Beresnevich, Levesley, and Ward (2021) pertaining to weighted simultaneous Diophantine approximation on manifolds.

We present a simple proof of some interpolation inequalities between H\"{o}lder and Lebesgue's spaces. As an example, to demonstrate the simplicity of their applications to nonlinear PDE, we give also a simple proof of an a-priory estimate…