Growth of the Maximum Modulus of Polynomials With Prescribed Zeros - Dewan, K. K.; Hans, Sunil (Sarajevo Journal of Mathematics, 2024)
If p(z) be a polynomial of degree n which does not vanish in the disk |z|<k, then for k=1, it is well known that align* _|z|=r<1|p(z)|&≥ (r+12)^n_|z|=1|p(z)|, and _|z|=R>1|p(z)|&≤ R^n+12_|z|=1|p(z)|.align* In this paper, we consider a class of lacunary polynomials and present certain generalizations as well as improvements of the above inequalities for the two cases k≥ 1 and k<1. 2000 Mathematics Subject Classification. 30A10, 30C10, 30C15