Abstract
In this paper we consider the problem of finding the estimate of maximum number of zeros in a prescribed region and the results which we obtain generalizes and improves upon some well known results.
Highlights
Introduction nLet p z ai zi be a polynomial of degree n such i 0 that an an 1 a1 a0 0 according to a well known result of Enstrom and Kakeya, the polynomial p z, does not vanish in z 1. concerning the number of zeros of the polynomial in the region z, the following result is due to Mohammad [1]. n in z, does not exceed1 log log 2 an aoDewan [2] generalized Theorem A to the polynomials with complex coefficients and obtained the following result.Theorem B
We prove the following
N n 1 1 0 , the number of zeros of p(z) in does not exceed
Summary
Concerning the number of zeros of the polynomial in the region z The following result is due to Theorem A. Let p z ai zi be a polynomial of i 0 degree n such that an an 1 a1 a0 0, the number of zeros of p z
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