On Cauchy’s bound for zeros of a polynomial

V. K. Jain, Kharagpur, India

Keywords: disc, generalization, zeroes of the polynomial AMS Subject classification: 30C15, 30C10

Abstract: Datt and Govil had improved Cauchy’s upper bound for the moduli of all the zeros of a polynomial of degree n. Guggenheimer had generalised that result due to Cauchy. We have obtained a generalization of the result due to Datt and Govil. At the same time, our generalisation turns out to be an improvement of Guggenheimer’s result also. Our result is best possible.