Related papers: A counterexample of two Romanov type conjectures

We confirm Martin's conjecture for a broad subclass of weakly quasi-o-minimal theories.

We prove a matrix inequality for matrix monotone functions, and apply it to prove a singular value inequality for Heinz means recently conjectured by X. Zhan.

We resolve a conjecture of Rystov concerning products of matrices, that generalizes the \v{C}ern\'y Conjecture.

We give a very simple proof of a strengthened version of Chernoff's Inequality. We derive the same conclusion from much weaker assumptions.

We prove a comparison isomorphism between singular cohomology and sheaf cohomology.

We prove Union-Closed sets conjecture.

We continue to discuss the example presented in \cite{JarPfl2015}. In particular, we clarify some gaps and complete the description of the Shilov boundary.

A counter example to the main result has been communicated to the author by Matei Toma.

We give a counterexample to the PIA (precise inversion of adjunction) conjecture for minimal log discrepancies. We also give a counterexample to the LSC conjecture for families.

In this note we elaborate on a recent counter-example to the Nelson-Seiberg theorem and to its generalizations. We provide sufficient conditions for the existence of such counter-examples, finding new ones. We claim that these…

I give an example showing that the recent claimed solution by Feder, Kinne and Rafiey to the CSP Dichotomy Conjecture is not correct.

We prove a series of Stephan's conjectures concerning Pascal triangle modulo 2 and give a polynomial generalization.

Arguably the simplest variation of this style of proof as we avoid reducing to the cubic case entirely.

Cox's well-known theorem justifying the use of probability is shown not to hold in finite domains. The counterexample also suggests that Cox's assumptions are insufficient to prove the result even in infinite domains. The same…

In this paper we first prove that a simple root of a polynomial satisfies the Sendov's conjecture. As the multiple roots trivially satisfy the Sendov's conjecture we conclude that the Sendov's conjecture holds true.

We give in this paper some squares of abelian surfaces that are counterexamples to a conjecture formulated by Zhang about the intersection of subvarieties and preperiodic points.

Zagier provided eleven conjectural rank two examples for Nahm's problem. All of them have been proved in the literature except for the fifth example, and there is no $q$-series proof for the tenth example. We prove that the fifth and the…

We state an improved version of the conjecture of Langlands and Rapoport, and we prove the conjecture for a large class of Shimura varieties. In particular, we obtain the first proof of the (original) conjecture for Shimura varieties of…

The main aim of the present paper is to disprove the Cohen--Lenstra--Martinet heuristics in two different ways and to offer possible corrections. We also recast the heuristics in terms of Arakelov class groups, giving an explanation for the…

We establish a reversal of Lyapunov's inequality for monotone log-concave sequences, settling a conjecture of Havrilla-Tkocz and Melbourne-Tkocz. A strengthened version of the same conjecture is disproved through counter example. We also…