Related papers: On Erd\"os--Szekeres problem and related problems

We survey the variants of Erd\H{o}s' distinct distances problem and the current best bounds for each of those.

In this paper, we formulate and prove several variants of the Erd\H{o}s-Tur\'{a}n additive bases conjecture.

We prove new results, related to the Littlewood and Mixed Littlewood conjectures in Diophantine approximation.

We show that an inequality related to Newton's inequality provides one more relation between skewness and kurtosis. This also gives simple and alternative proofs of the bounds for skewness and kurtosis.

This note presents a new proof of the well-known Strichartz estimates for the Schr\"odinger equation in $2+1$ dimensions, building on ideas from our recent work \cite{MO}.

This is a quick survey of theoretical and experimental efforts to understand and identify the Odderon.

We prove new general results on sumsets of sets having Szemer\'edi--Trotter type. This family includes convex sets, sets with small multiplicative doubling, images of sets under convex/concave maps and others.

Certain excess versions of the Minkowski and H\"older inequalities are given. These new results generalize and improve the Minkowski and H\"older inequalities.

The original proof of the Sharkovsky theorem is presented in full detail. The proof should be accessible to readers with basic Real Analysis background. Although nowadays there are several alternative proofs of this classical result, we…

We give a short proof of a strengthening of the Maximal Ergodic Theorem which also immediately yields the Pointwise Ergodic Theorem.

We provide a proof of a variant of the Landau-Siegel Zeros conjecture.

In this article, we discuss and survey the recent progress towards the Schottky problem, and make some comments on the relations between the Andr{\'e}-Oort conjecture, Okounkov convex bodies, Coleman's conjecture, stable modular forms,…

This note gives an informal overview of the proof in our paper "Borel Conjecture and Dual Borel Conjecture", see arXiv:1105.0823.

We persist in our investigation of the sup-completion of a Dedekind complete Riesz space, extending to the broader context of Riesz spaces. some results initially obtained by Feng, Li, Shen, and also by Erd\"os, and R\'enyi.

We give a simple proof of a recently result concerning Hardy $q$-inequalities.

The purpose of this short note is to provide a new and very short proof of a result by Sudakov, offering an important improvement of the classical result by Kolmogorov-Riesz on compact subsets of Lebesgue spaces.

In this paper we consider Erd\"os-Mordell inequality and its extension in the plane of triangle to the Erd\"os-Mordell curve. Algebraic equation of this curve is derived, and using modern computer tools in mathematics, we verified one…

A very short and direct proof along the lines of the Kamae-Katznelson-Weiss approach.

In this note we briefly survey and propose some open problems related to isoparametric theory.

We prove the Erdos-Turan equidistribution inequality, using a construction due to Chebyshev, Markov, and Stieltjes. The method is applicable in a more general setting. As an example, we state another inequality that can be proved using this…