ON SOME BOUNDS FOR ZEROS OF NORM-BOUNDED POLYNOMIALS

We define a region H(alpha, f) in the complex number field, where alph a is a complex number, f(x) is-an-element-of K[x] and f(alpha) not-equ al 0. The region H(alpha,f) contains no zeros of f(x) and is relativel y easy to analyze. We analyze the region with respect to K = R and K = C. By the results of the analysis, we derived some bounds for zeros o f f(x) from the norm of f(x). The region H(alpha, f) can be used for t he analysis of the distribution of zeros of polynomials over integers whose norms and degrees are bounded. For these polynomials, we calcula ted the distributions of their zeros by computer and compared them wit h the regions. For several cases the regions describe the distribution s well. However, there are some cases where the regions do not describ e well.