相关论文: Proof of a conjecture of Hadwiger

We prove the Aharoni Berger Conjecture

A false application of Proposition 4.10 causes a mistake in the proof of Corollary 4.11

The paper presents a counterexample to the Hodge conjecture.

A proof of Sendov's conjecture is given.

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

A short, fairly self-contained proof is given of the Poincar\'e Conjecture. In the previous version there was an error on Page 8. This gap has now been filled.

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…

In this short note, we prove Hadwiger's conjecture for strongly monotypic polytopes.

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

We do not know whether the main result is true, the proof of theorem 2.1 contains a gap.

Based on the results people have obtained, we try to prove the Jacobian conjecture, but there is a gap in the proof.

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

withdrawed due to a substantial error.

The proofs of Theorem 1.1 and Theorem 1.5(2) in the authors' paper 'The Hasse norm principle for abelian extensions' are incorrect. We point out the mistakes and provide correct proofs, using techniques of the original paper.

This paper has been withdrawn by the authors due to crucial error in the main proof (located in Section 2.4). The authors apologize for any inconveniences.

Reason for withdrawal: There is a serious mistake in the calculation of the divisor of the rational section used in the proof of Prop. 2.2.1., and with the correct value the argument does not work.

In this paper the circulant Hadamard conjecture is proved.

Over one year ago, a very long preprint posted on arXiv [arXiv:1709.03771] and HAL announced a proof of Lehmer's Conjecture (and of other related results). Unfortunately, as was remarked by several specialists, this proof contains a (at…

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

There is a serious mistake in the proof.