相关论文: Note on the location of zeros of polynomials

In this paper, we are concerned with the problem of locating the zeros of polynomials of a quaternionic variable with quaternionic coefficients. We derive some new Cauchy bounds for the zeros of a polynomial by virtue of maximum modulus…

Locating the zeros of quaternionic polynomials is a fundamental problem with significant implications across scientific and engineering disciplines, yet the noncommutative nature of quaternion multiplication makes it fundamentally more…

In this paper we investigate distribution of zeros for only quasipolynom and obtain exactly lower-bound for their modulus.

In this paper we investigate distribution of zeros for once quasipolynom and obtain exactly lower-bound for their modulus.

We discuss existence of explicit search bounds for zeros of polynomials with coefficients in a number field. Our main result is a theorem about the existence of polynomial zeros of small height over the field of algebraic numbers outside of…

Many upper bounds for the moduli of polynomial roots have been proposed but reportedly assessed on selected examples or restricted classes only. Regarding quality measured in terms of worst-case relative overestimation of the maximum…

We estimate the number of zeros of a polynomial in $\mathbb{C}[z]$ within any small circular disc centered on the unit circle, which improves and comprehensively extends a result established by Borwein, Erd{\'e}lyi, and Littmann~\cite{BE1}…

In this work, we are dealing with some properties relating the zeros of a polynomial and its Mahler measure. We provide estimates on the number of real zeros of a polynomial, lower bounds on the distance between the zeros of a polynomial…

We establish asymptotic upper bounds on the number of zeros modulo $p$ of certain polynomials with integer coefficients, with $p$ prime numbers arbitrarily large. The polynomials we consider have degree of size $p$ and are obtained by…

Some new bounds for the extreme zeroes of Jacobi polynomials are obtained with an elementary approach. A feature of these bounds is their simple forms, which make them easy to work with. Despite their simplicity, our lower bounds for the…

Finding an approximate region containing all the zeros of analytic polynomials is a well-studied problem. But the numb er of the zeros and regions containing all the zeros of complex-valued harmonic polynomials is relatively a fresh…

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.

We describe the limit zero distributions of sequences of polynomials with positive coefficients.

We obtain bounds for the numerical radius of $2 \times 2$ operator matrices which improve on the existing bounds. We also show that the inequalities obtained here generalize the existing ones. As an application of the results obtained here…

Let $p(z)=a_0+a_1z+a_2z^2+a_3z^3+\cdots+a_nz^n$ be a polynomial of degree $n,$ where the coefficients $a_j,$ $j \in \{0,1,2,\cdots n\},$ may be complex. We impose some restriction on the coefficients of the real part of the given polynomial…

In this article, we propose a few sufficient conditions on polynomials having integer coefficients all of whose zeros lie outside a closed disc centered at the origin in the complex plane and deduce the irreducibility over the ring of…

In this paper, we derive new bounds for the zeros of quaternionic polynomials by applying localization theorems, which includes Gershgorin-type theorems for the left eigenvalues of matrices of left monic quaternionic polynomials. These…

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…

Let S be a finite subset of a field. For multivariate polynomials the generalized Schwartz-Zippel bound [2], [4] estimates the number of zeros over Sx...xS counted with multiplicity. It does this in terms of the total degree, the number of…

Let $p(z)=z^n+a_{n-1}z^{n-1}+a_{n-2}z^{n-2}+\ldots+a_1z+a_0$ be a complex polynomial with $a_0\neq 0$ and $n\geq 3$. Several new upper bounds for the moduli of the zeros of $p$ are developed. In particular, if…