相关论文: A proof of Sendov's conjecture
We provide a proof and a counterexample to two conjectures made by N. Kuznetsov.
In this paper we first prove that a simple root of a polynomial satisfies the Sendov's conjecture. As the multiple roots trivially satisfy the Sendov's conjecture we conclude that the Sendov's conjecture holds true.
Recently GM Sofi & SA Shabir [arXive: 1903.01850v2 [math.GM] 6 Mar 2019] made an attempt to prove the Sendov's conjecture. But unfortunately the proof is not correct. In this note, we discuss the fallacy in the proof.
In this paper, we prove the Sendov conjecture for polynomials of degree nine. We use a new idea to obtain new upper bound for the $\sigma-$sum to zeros of the polynomial.
We provide a proof of a variant of the Landau-Siegel Zeros conjecture.
The article presents the proof of Casas-Alvero conjecture.
We prove the Aharoni Berger Conjecture
A proof is given of Rosenthal's \(\ell_1\) theorem.
We prove Union-Closed sets conjecture.
In this paper the circulant Hadamard conjecture is proved.
The Sendovs conjecture asserts that if all the zeros of a polynomial p(z) lie in the closed unit disk, then there must be a critical point of p(z) within unit distance of each zero. The conjecture has been proved to be true for many special…
Sendov's conjecture, which was first introduced in the last 50s, asserts that if all the zeros of a polynomial $p$ lie in the closed unit disk then for each zero there must be a critical point of $p$ within unit distance. This paper…
We provide a proof of the Borwein Conjecture using analytic methods.
We prove Simon's conjecture for 3-manifolds.
In this paper, we obtain new results on the critical points of a polynomial, these results are useful to the Sendov conjecture.
We prove non-archimedean analogue of Sendov's conjecure. We also provide complete list of polynomials over an algebraically closed non-archimedean field $K$ that satisfy the optimal bound in the Sendov's conjecture.
A vector variational principle is proved.
We settle in the affirmative the Graham-Sloane conjecture.
In this note, we present a simple directed graph proof of Sharkovsky's theorem.
The paper contains an alternative proof of M. Kontsevich Formality Theorem.