Related papers: Landis' conjecture: a survey

In this paper we attack the Erdos-Straus conjecture by means of the structure of its solutions, extending and improving the results of a previous paper. Using previous results and supported by the works of Elsholtz and Tao and Monks and…

We obtain new average results on the conjectures of Lang-Trotter and Sato-Tate about elliptic curves.

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

In this paper we investigate the recent advances by Zhang, Maynard and Pintz towards Polignac's conjecture and give some new results concerning the relationship between Polignac numbers and arithmetic progressions.

A proof of Sendov's conjecture is given.

In a very celebrated paper A. Connes has formulated a conjecture which is now one of the most important open problem in Operator Algebras. This importance comes from the works of many mathematicians who have found some unexpected equivalent…

This article is an overview of the geometrization conjecture for the local Langlands correspondence formulated by the author.

We will prove the Brannan conjecture for particular values of the parameter. The basic tool of the study is an integral representation published in a recent work [3].

In this article, we continue our investigation into the unique continuation properties of real-valued solutions to elliptic equations in the plane. More precisely, we make another step towards proving a quantitative version of Landis'…

In this paper, we proved a special case of the DDVV Conjecture.

In this work, we study the Landis conjecture for second-order elliptic equations in the plane. Precisely, assume that $V\ge 0$ is a measurable real-valued function satisfying $\|V\|_{L^\infty({\mathbb R}^2)} \le 1$. Let $u$ be a real…

In this paper we prove a quantitative form of Landis' conjecture in the plane. Precisely, let $W(z)$ be a measurable real vector-valued function and $V(z)\ge 0$ be a real measurable scalar function, satisfying $\|W\|_{L^{\infty}({\mathbf…

First a few reformulations of Frankl's conjecture are given, in terms of reduced families or matrices, or analogously in terms of lattices. These lead naturally to a stronger conjecture with a neat formulation which might be easier to…

Confounder selection is perhaps the most important step in the design of observational studies. A number of criteria, often with different objectives and approaches, have been proposed, and their validity and practical value have been…

In this paper, by making use of one of Chen's theorems and the method of mathematical analysis, we refine Edwards-Child's inequality and solve a conjecture posed by Liu.

This short survey contains some recent developments of the algebraic theory of racks and quandles. We report on some elements of representation theory of quandles and ring theoretic approach to quandles.

This is a survey article on the Hardy-Littlewood conjecture about primes in quadratic progressions. We recount the history and quote some results approximating this hitherto unresolved conjecture.

We provide empirical evidence for the Erd\H{o}s-Straus conjecture by improving computational bounds to $10^{18}$ and by evaluating the solution-counting function $f(p)$ for this conjecture.

We consider estimation procedures which are recursive in the sense that each successive estimator is obtained from the previous one by a simple adjustment. We propose a wide class of recursive estimation procedures for the general…

This is a survey on the Farrell-Jones Conjecture about the algebraic K- and L-theory of groups rings and its applications to algebra, geometry, group theory, and topology.