Related papers: Hebey-Vaugon conjecture II
In this paper we propose a conjecture concerning partial sums of an arbitrary finite subset of an abelian group, that naturally arises investigating simple Heffter systems. Then, we show its connection with related open problems and we…
In this paper the circulant Hadamard conjecture is proved.
This article is a collected information from some books and papers, and in most cases the original sentences is reserved about twin prime conjecture.
We briefly review an open conjecture about Higgs bundles that are semistable with after pulling back to any curve, and prove it in the rank 2 case. We also prove a set of inequalities holding for H-nef Higgs bundles that generalize some of…
This note gives an informal overview of the proof in our paper "Borel Conjecture and Dual Borel Conjecture", see arXiv:1105.0823.
We outline an approach to prove the two dimensional Jacobian Conjecture using the theory of fractals.
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…
We survey the state of the union-closed sets conjecture.
This is a survey on Kawaguchi-Silverman conjecture.
We prove several extensions of the Erdos-Fuchs theorem.
In this paper, we present a possible theoretical explanation for benford's law. We develop a recursive relation between the probabilities, using simple intuitive ideas. We first use numerical solutions of this recursion and verify that the…
We show that the Jacobian conjecture of the two dimensional case is true.
We give a counterexample to a recently conjectured variant of the Penrose inequality.
In this paper, we pose many challenging conjectures on congruences involving binomial coefficients and Ap\'ery-like numbers.
We provide a proof of a variant of the Landau-Siegel Zeros conjecture.
We prove the Invariant Subspace Conjecture for separable Hilbert spaces.
We study the Mathieu Conjecture for $SU(2)$ using the matrix elements of its unitary irreducible representations. We state a conjecture for the particular case $SU(2)$ implying the Mathieu Conjecture for $SU(2)$.
Using algebraic transformations and equivalent reformulations we derive a number of new results from some earlier ones (by the author) in more accepted terms closely related to well-known conjectures of Bondy and Jung including a number of…
We give a new proof of some cases of the Baum-Connes conjecture along the lines of a proof of the Farrell-Jones conjecture.
An integral transformation relating two inequalities in Khabibullin's conjecture is found. Another proof of this conjecture for some special values of its numeric parameters is suggested.