Related papers: The Brumer--Stark Conjecture over Z
In this paper, we study the Br\"{u}ck conjecture \cite{Bruck-1996} by interpreting it through solutions of first-order partial differential equations in several complex variables. Our results show that the Br\"{u}ck conjecture…
We study algebras on which the Berenstein-Zelevinsky conjecture is true. In particular, we prove that this conjecture is true "up to localization".
Let $F$ be a totally real field and $K$ a finite abelian CM extension of $F$. Using class field theory, we show that our previous result giving a strong form of the Brumer-Stark conjecture implies the minus part of the equivariant Tamagawa…
We prove a conjecture of Zuber on the signature of intersection froms associated with affine algebras of type A.
We prove the Invariant Subspace Conjecture for separable Hilbert spaces.
We prove a Freiman--Ruzsa-type theorem with polynomial bounds in arbitrary abelian groups with bounded torsion, thereby proving (in full generality) a conjecture of Marton. Specifically, let $G$ be an abelian group of torsion $m$ (meaning…
We present a new conjecture for the $SU_q(N)$ Perk-Schultz models. This conjecture extends a conjecture presented in our article (Alcaraz FC and Stroganov YuG (2002) J. Phys. A vol. 35 pg. 6767-6787, and also in cond-mat/0204074).
We give a proof of the Marker-Steinhorn Theorem which fills a gap in previous proofs of the result.
We settle in the affirmative the Graham-Sloane conjecture.
We prove a conjecture by D. Zeilberger on the determinant of a certain matrix and relate it to a problem of non-existence of 1-cycles in this note.
We give a proof of the Greene-Krantz conjecture on convex domains in $\CC^2$. Curiously, the proof technique depends on subelliptic estimates for the $\bar{\partial}$ problem.
We prove \emph{the other half} of Brauer's Height Zero Conjecture in the case of principal blocks.
Several results about the union-closed sets conjecture are presented.
In this paper, we obtained an equivalent proposition of Brennan`s conjecture. And given two lower bound estimation of the conjecture one of them connected with Schwarzian derivative. The present study also verified the correctness of the…
In this paper, we give a new and short proof of a Theorem on k-hypertournament losing scores due to Zhou et al.[7].
This is a survey on Kawaguchi-Silverman conjecture.
We complete the proof of Brauer's Height Zero Conjecture from 1955 by establishing the open implication for all odd primes.
This is a survey on Sarnak's Conjecture
The purpose of this note is to give an affirmative answer to a conjecture appearing in [Integral Transforms Spec. Funct. 26 (2015) 90-95].
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.