Related papers: A Note on the Paper "Localization of Zeros of Pola…
We derive a useful result about the zeros of the $k$-polar polynomials on the unit circle; in particular we obtain a ring shaped region containing all the zeros of these polynomials. Some examples are presented.
In this note, we give the possible revised version of the unique solvability conditions for the two incorrect results that appeared in the published paper by Wu et al. (Appl Math Lett 76:195-200, 2018).
The main purpose of this paper is to present the generalization of the inequalities between the modulus of the polar derivative and the polynomial itself, depending on consideration of the zeros inside and outside of a closed disk and the…
The purpose of this note is to point out that the main result of [M. Chamberland, When Are All the Zeros of a Polynomial Real and Distinct? Amer. Math. Monthly. 127 (2020) 449-451] is implicitly contained in the elementary lore of the…
In [1] we highlighted the fact that the log polynomial expansion employed in Nature Astron. 3, no.3, 272-277 (2019) [2] is a poor approximation to flat $\Lambda$CDM, so using it to infer deviations from flat $\Lambda$CDM is not…
In this note, we provide a wide range of upper bounds for the moduli of the zeros of a complex polynomial. The obtained bounds complete a series of previous papers on the location of zeros of polynomials.
The purpose of this note is to revive in $L^p$ spaces the original A. Markov ideas to study monotonicity of zeros of orthogonal polynomials. This allows us to prove and improve in a simple and unified way our previous result [Electron.…
This paper has been withdrawn by the author due to an error in the main proof (thanks to Carlos D'Andrea)
In this Note, we provide the comments on the paper [A note on the hit problem for the polynomial algebra in the case of odd primes and its application] which was published in the RACSAM [Rev. Real. Acad. Cienc. Exactas. Fis. Nat. Ser.…
This set of notes re-proves known results on weighted automata (over a field, also known as multiplicity automata). The text offers a unified view on theorems and proofs that have appeared in the literature over decades and were written in…
In this paper we relate the location of the complex zeros of the reliability polynomial to parameters at which a certain family of rational functions derived from the reliability polynomial exhibits chaotic behaviour. We use this connection…
By addressing a long-standing open problem, listed in a highly regarded collection of open questions in the field and described as a "worthwhile research project", this note extends Markov's theorem (Markoff, Math. Ann., 27:177-182, 1886)…
The analysis of solutions to algebraic equations is further simplified. A couple of functions and their analytic continuation or root findings are required.
The authors present a unified method for calculating the zeros of the classical orthogonal polynomials based upon the electrostatic interpretation and its connection to the energy minimization problem. Examples are given with error…
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 prove that for large $n$, all but $o(2^{n})$ polynomials of the form $P(z) = \sum_{k=0}^{n-1}\pm z^k$ have $n/2 + o(n)$ roots inside the unit disk. This solves a problem from Hayman's book 'Research Problems in Function Theory' (1967).
We study noncommutative versions of holomorphic and harmonic functions on the unit disk.
We study distribution of zeros of a complex polynomial whose coefficients has been modified. We give a new proof of the theorem of Rubinstein, and with similar method we prove a new theorem that is not generalization of the previous…
We provide a simple method to recognize classical orthogonal polynomials on lattices defined only by their coefficients of the three term recurrence relation.
Using Singular Rescaling We Prove Some Bifurcation Results. This note Presents short proofs for some Bifurcation results which had been appeared with other authors.