Related papers: A note on a recent attempt to prove Sendov's conje…

A proof of Sendov's conjecture is given.

Recently Shekhar Suman [arXiv: 2407.07121v6 [math.GM] 3 Aug 2024] made an attempt to prove the irrationality of $\zeta(5)$. But unfortunately the proof is not correct. In this note, we discuss the fallacy in the proof.

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.

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.

In this note, we establish the validity of a conjecture recently proposed in Mathematics Magazine and connect it to the existing interesting results

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…

In this paper we study a particular class of polynomials. We study the distribution of their zeros, including the zeros of their derivatives as well as the interaction between this two. We prove a weak variant of the sendov conjecture in…

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.

The paper presents a counterexample to the Hodge conjecture.

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

Based on the results people have obtained, we try to prove the Jacobian conjecture, but there is a gap in the proof.

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

The present note refers to a result proposed in [Elhadj and Sprott, 2012], and shows that the Theorem therein is not correct. We explain that a proof of that Theorem cannot be given, as the statement is not correct, and we underline a…

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

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

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…

New cases of the multiplicity conjecture are considered.

The original version of the paper claimed to disprove the pseudo-Riemannian Lichnerowicz conjecture of D'Ambra and Gromov. However, the argument contains a crucial sign error in the lines following equation (8).

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

In this note, we present a simple non-directed graph proof of Sharkovsky's theorem which is different from the one given in [2].