Related papers: A note on the Hodge conjecture

Paper withdrawn by the author.

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

In this short note we give counterexamples to several results related to extension theorems published recently.

In this paper we propose counterexamples to the Geometrization Conjecture and the Elliptization Conjecture.

The paper gives a counter-example to the relative version of the Manin-Mumford conjecture.

We give an explicit counterexample to an entanglement inequality suggested in a recent paper [quant-ph/0005126] by Benatti and Narnhofer. The inequality would have had far-reaching consequences, including the additivity of the entanglement…

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

In this note, we establish the validity of a conjecture recently proposed in Mathematics Magazine and connect it to the existing interesting results

In this note we prove a converse of Bohr's equivalence theorem for Dirichlet series under some natural assumptions.

The paper contains an alternative proof of M. Kontsevich Formality Theorem.

We prove a recent conjecture by Ulas on reducible polynomial substitutions.

In this note, we disprove two Romanov type conjectures posed by Chen.

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

This is an appendix to our paper "An update of the Hirsch Conjecture" (arXiv:0907.1186), containing proofs of some of the results and comments that were omitted in it.

In this note we provide some results related to the Koethe conjecture and exhibit that the condition R satisfies the Koethe conjecture given in [2, theorem 2.6 ] is superfluous at least under certain conditions described in this note.

A conjecture regarding the structure of expander graphs is discussed.

In this paper the circulant Hadamard conjecture is proved.

The Hodge conjecture is shown to be equivalent to a question about the homology of very ample divisors with ordinary double point singularities. The infinitesimal version of the result is also discussed.

In this paper we use computational methods to disprove a conjecture by Alaoglu and Erd\H{o}s regarding the superabundant numbers.

In this note, we propose a conjecture stating that some series involving primitive sequences are convergent. Then, we show (by a counterexample) that the analogue of a conjecture of Erd\H{o}s, for those series, is false.