Related papers: A simple proof of a conjecture on univariate polyn…

In this paper we prove Shapiro's 1958 Conjecture on exponential polynomials, assuming Schanuel's Conjecture.

This paper has been withdrawn by the author due to an error in the last paragraph of step 2 of the main proof, on page 6.

This article has been withdrawn due to a mistake which is explained in version 2.

This brief note corrects some errors in the paper quoted in the title, highlights a combinatorial result which may have been overlooked, and points to further improvements in recent literature.

This paper has been withdrawn by the author due to an error in the proof of Theorem 1.

The author was informed that the result in the original version had been obtained earlier by K. Ueda (arXiv:math/0503355 [math.AG]). The paper is retracted.

In 2007, Dmytrenko, Lazebnik and Williford posed two related conjectures about polynomials over finite fields. Conjecture~1 is a claim about the uniqueness of certain monomial graphs. Conjecture~2, which implies Conjecture~1, deals with…

A very simple and short proof of the polynomial matrix spectral factorization theorem (on the unit circle as well as on the real line) is presented, which relies on elementary complex analysis and linear algebra.

Admin note: withdrawn by arXiv admin because of the use of a pseudonym, in violation of arXiv policy.

This paper has been withdrawn by the author, due to a crucial error in the proof of Lemma 3.1.

This paper has been withdrawn by the author. The statement of the Main Theorem but is wrong in general, there have been provided counterexamples. The main theorem only holds conditionally, under the finiteness statement of theorem 2.8.

In this paper a result of Latala about the tail behavior of Gaussian polynomials will be discussed. Latala proved an interesting result about this problem in paper [2]. But his proof applied an incorrect statement at a crucial point. Hence…

This paper has been withdrawn by the author, due to errors in the figures.

This paper has been withdrawn by the author. The conjecture follows from the finiteness of group von Neumann algebras.

This paper has been withdrawn by the authors because M. Aschenbrenner pointed out that the proof of theorem 3.1 was incorrect.

This paper has been withdrawn by the author(s), due the final version in math.QA/0604564

The paper has been withdrawn due to an error in the main theorem.

The Casas-Alvero conjecture states that if $f(X)$ is a monic univariate polynomial of degree $d$ over a characteristic $0$ field $\mathbb{K}$ such that $\gcd(f, f_{i})$ is non-trivial for each $i=1, \dots, d-1$, then $f(X)=(X-\alpha)^d$ for…

The paper is withdrawn. The proof has an error and it requires a different approach.

An elementary gap in the proof of corollary 2.2 was found, the claim in the first version of the paper is thus retracted.