Related papers: A simple proof of a conjecture on univariate polyn…
This paper has been withdrawn by the authors due to an error in Section 7.
This paper has been withdrawn by the author due to a crucial error.
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.
Over a field of characteristic zero, it is clear that a polynomial of the form (X-a)^d has a non-trivial common factor with each of its d-1 first derivatives. The converse has been conjectured by Casas-Alvero. Up to now there have only been…
This paper has been withdrawn by the author due to a crucial error.
This paper has been withdrawn by the author due to a gap in the proof of the main result.
This paper has been withdrawn by the author due to a crucial error in the last lines in the proof of Lemma 3.3.
This paper has been withdrawn by the authors due to the fact that the conjecture has indeed already long been established.
Univariate polynomials with only real roots -- while special -- do occur often enough that their properties can lead to interesting conclusions in diverse areas. Due mainly to the recent work of two young mathematicians, Julius Borcea and…
We investigate necessary and sufficient conditions for an arbitrary polynomial of degree $n$ to be trivial, i.e. to have the form $a(z-b)^n$. These results are related to an open problem, conjectured in 2001 by E. Casas- Alvero. It says,…
This paper has been withdrawn by the author(s), due a crucial sign error in Thm. 11.
We present a theorem about irreducibility of a polynomial that is the resultant of two others polynomials. The proof of this fact is based on the field theory. We also consider the converse theorem and some examples.
The Casas-Alvero conjecture is about interpolation polynomials. There are some partial proofs of it, but there is not any proof in the general case.In this paper we propose three.
This paper has been withdrawn by the author due to an erro thereon line -2 of page 4.
We conjecture that the roots of a degree-n univariate complex polynomial are located in a union of n-1 annuli, each of which is centered at a root of the derivative and whose radii depend on higher derivatives. We prove the conjecture for…
The Casas-Alvero conjecture says that a degree $n$ complex univariate polynomial sharing a root with each of its derivative must have only one root. In this article we give three results. The first one, is that the number of possible…
This paper has been withdrawn by the author, due to an error in the proof of Theorem 3.8.
The purpose of this note is to give an affirmative answer to a conjecture appearing in [Integral Transforms Spec. Funct. 26 (2015) 90-95].
This paper has been withdrawn by the author due to some errors.
This paper has been withdrawn by the author due to an error in the proof of Theorem 6.