Recent Progress in the Study of Polynomials with Constrained Coefficients

Abstract

This survey gives a taste of the author’s recent work on polynomials with constrained coefficients. Special attention is paid to unimodular, Littlewood, Newman, Rudin-Shapiro, and Fekete polynomials, their flatness and ultraflatness properties, their Lq norms on the unit circle including Mahler’s measure, and bounds on the number of unimodular zeros of self-reciprocal polynomials with coefficients from a finite set of real numbers. Some interesting connections are explored, and a few conjectures are also made.