منابع مشابه
On the Location of Zeros of Polynomials
then P z has all the zeros in z t . In the literature, [1-15], there exist extensions and generalizations of Eneström-Kakeya theorem. Joyal, Labelle and Rahman [9] extended this theorem to polynomials whose coefficients are monotonic but not necessarily non negative and the result was further generalized by Dewan and Bidkham [6] to read as: Theorem B. If =0 := n j j j P z a z is a p...
متن کاملZeros of Random Polynomials On
For a regular compact set K in C and a measure μ on K satisfying the Bernstein-Markov inequality, we consider the ensemble PN of polynomials of degree N , endowed with the Gaussian probability measure induced by L(μ). We show that for large N , the simultaneous zeros of m polynomials in PN tend to concentrate around the Silov boundary of K; more precisely, their expected distribution is asympto...
متن کاملOn the Zeros of Self-Inversive Polynomials
A classical result due to Cohn states that a self-inversive polynomial has all its zeros on the unit circle if and only if all the zeros of its derivative lie in the closed unit disk. A more flexible necessary and sufficient condition than that of Cohn’s was given by Chen. However those results do not give any information on the simplicity of zeros of a self-inversive polynomial. This paper mod...
متن کاملOn the Zeros of Plane Partition Polynomials
Over the past ten years, many examples of natural polynomial families from combinatorics and number theory have emerged whose zeros for high degrees appear to converge to intriguing curves in the complex plane. One interesting collection of examples appears on the website [16] of Richard Stanley which includes chromatic polynomials of complete partite graphs, q-analogue of Catalan numbers, Bern...
متن کاملSome compact generalization of inequalities for polynomials with prescribed zeros
Let $p(z)=z^s h(z)$ where $h(z)$ is a polynomial of degree at most $n-s$ having all its zeros in $|z|geq k$ or in $|z|leq k$. In this paper we obtain some new results about the dependence of $|p(Rz)|$ on $|p(rz)| $ for $r^2leq rRleq k^2$, $k^2 leq rRleq R^2$ and for $Rleq r leq k$. Our results refine and generalize certain well-known polynomial inequalities.
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ژورنال
عنوان ژورنال: Communications, Faculty Of Science, University of Ankara Series A1Mathematics and Statistics
سال: 1977
ISSN: 1303-5991
DOI: 10.1501/commua1_0000000272