학술논문
Growth of polynomials with prescribed zeros.
Document Type
Journal
Author
Dewan, K. K. (6-JMINS) AMS Author Profile; Ahuja, Arty (6-JMINS) AMS Author Profile
Source
Subject
26 Real functions -- 26C Polynomials, rational functions
26C05Polynomials: analytic properties, etc.
30Functions of a complex variable -- 30C Geometric function theory
30C15Zeros of polynomials, rational functions, and other analytic functions
26C05
30
30C15
Language
English
Abstract
Summary: ``In this paper, we study the growth of polynomials of degree $n$ having all their zeros on $\vert z\vert =k$, $k\le1$. Using the notation $M(p,t)=\max_{\vert z\vert=t}\vert p(z)\vert $, we measure the growth of $p$ by estimating $\left\{\frac{M(p,t)}{M(p,1)}\right\}^s$ from above for any $t\ge1$, $s$ being an arbitrary positive integer.''