Related papers: A Note on a Recent Conjecture in Mathematics Magaz…

New cases of the multiplicity conjecture are considered.

In this paper, we survey some recent results on the Artin conjecture and discuss some aspects for the Artin conjecture.

We survey recent developments on the Restriction conjecture.

We collect here various conjectures on congruences made by the author in a series of papers, some of which involve binary quadratic forms and other advanced theories. Part A consists of 100 unsolved conjectures of the author while…

The purpose of this note is to give an affirmative answer to a conjecture appearing in [Integral Transforms Spec. Funct. 26 (2015) 90-95].

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

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…

The paper presents a counterexample to the Hodge conjecture.

We put a new conjecture on primes from the point of view of its binary expansions and make a step towards justification.

A conjecture is given that, if true, could lead to an algorithm for computing definite sums of rational functions.

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

We discuss the validity of the proof of the fixed numerator conjecture on Markov numbers, which is the main result of the paper mentioned in the title.

We provide new sufficient conditions under which Ryser's conjecture holds.

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

In a recent paper published in the Philosophical Magazine [Z.-D. Zhang, Phil. Mag. 87, 5309-5419 (2007), arXiv:0705.1045], the author advances a conjectured solution for various properties of the three-dimensional Ising model. Here we…

In this paper, we give a survey of the recent develpoments of the DDVV conjecture.

We review a combinatoric approach to the Hodge Conjecture for Fermat Varieties and announce new cases where the conjecture is true.

Two conjectures recently proposed by one of the authors are disproved

We show that some mathematical results and their negations are both deducible. The derived contradictions indicate the inconsistency of current mathematics. This paper is an updated version of arXiv:math/0606635v3 with additional results…

The purpose of this short note is to present a simplified proof of Serre's modularity conjecture using the strong modularity lifting results currently available. This second version includes extra details on definitions and proofs than the…