Related papers: A counterexample of two Romanov type conjectures

We provide a proof and a counterexample to two conjectures made by N. Kuznetsov.

In this note we investigate the Cheltsov--Rubinstein conjecture. We show that this conjecture does not hold in general and some counterexamples will be presented.

The paper presents a counterexample to the Hodge conjecture.

We answer negatively a 2014 problem of Yang and Chen on Romanoff type representations. Sharp results involving their problem were also obtained in this article.

We give a counterexample to a recently conjectured variant of the Penrose inequality.

A conjecture of Woods from 1972 is disproved.

We give counterexamples to Okounkov's log-concavity conjecture for Littlewood-Richardson coefficients.

In this paper we prove two conjectures stated by Chao-Ping Chen in [Int. Trans. Spec. Funct. 23:12 (2012), 865--873], using a method for proving inequalities of mixed trigonometric polynomial functions.

We prove that the Laptev--Safronov conjecture (Comm. Math. Phys., 2009) is false in the range that is not covered by Frank's positive result (Bull. Lond. Math. Soc., 2011). The simple counterexample is adaptable to a large class of…

The article provides a counterexample to a conjecture by Blocki-Zwonek.

We obtain some results related to Romanoff's theorem.

Two conjectures recently proposed by one of the authors are disproved

The original version of the paper claimed to disprove the pseudo-Riemannian Lichnerowicz conjecture of D'Ambra and Gromov. However, the argument contains a crucial sign error in the lines following equation (8).

In this short note we present a family of counterexamples to the King's conjecture.

This note points out that the assertions of [1] are groundless and incorrect.

A proof of Sendov's conjecture is given.

In this article, we give two different proofs of why the Collatz Conjecture is false.

Paper withdrawn by the author.

In this very short note, we give a counterexample to a recent conjecture of Gilmer which would have implied the union-closed conjecture.

We show that the analogue of the Peterson conjecture on the action of Steenrod squares does not hold in motivic cohomology.