Location of zeros of a Lacunary type polynomial

Abstract

For a given polynomial p(z) of degree n with real or complex coefficients, our basic aim has been to determine the smallest region in which all the zeros of p(z) lie. In the present paper, we have obtained a result by using Lacunary type polynomial which gives the region of zeros neither circular nor annular except in some particular cases. Our result plays an important role to reduce the region of polynomial zeros.