相关论文: A proof of Sendov's conjecture

The Sendov conjecture asserts that if all the zeros of a polynomial p lie in the closed unit disk then there must be a zero of p ' within unit distance of each zero. In this paper we give a partial result when p has simple zeros.

In this paper, we obtain new results on the critical points of a polynomial. We discuss the Sendov conjecture for polynomials of degree nine.

Sendov's conjecture asserts that if a complex polynomial $f$ of degree $n \geq 2$ has all of its zeroes in closed unit disk $\{ z: |z| \leq 1 \}$, then for each such zero $\lambda_0$ there is a zero of the derivative $f'$ in the closed unit…

In this article, we prove a weighted version of Saitoh's conjecture. As an application, we prove a weighted version of Saitoh's conjecture for higher derivatives.

A simple proof of Egorov's theorem for infinite measure is given

We provide a short proof of the 1-dimensional flat chain conjecture.

Error in proof of theorem 10.

In this article, we give a proof on the Arnold-Chekanov Lagrangian intersection conjecture on the cotangent bundles and its generalizations.

The paper presents a counterexample to the Hodge conjecture.

The article provides a counterexample to a conjecture by Blocki-Zwonek.

Sendov conjecture tells that if $P$ denotes a complex polynomial having all his zeros in the closed unit disk and $a$ denote a zero of $P$, the closed disk of center $a$ and radius 1 contains a zero of the derivative $P'$. The main result…

We present a relative form of the Toponogov comparison theorem.

In this paper, we prove a conjecture of Schnell in the surface case.

We consider the conjecture of Brutman and Pasow on a totality divided differences and prove the conjecture for continuous functions.

We give a proof of some small weight and level cases of Serre's conjecture.

We prove a variation of Gronwall's lemma.

Recently we have obtained two simple proofs of Sharkovsky's theorem, one with directed graphs [7] and the other without [8]. In this note, we present yet more simple proofs of Sharkovsky's theorem.

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

We obtain some results related to Romanoff's theorem.

In this note we give a detailed proof of a theorem of Aubin.