Coppersmith-Rivlin type inequalities and the order of vanishing of polynomials at 1

TL;DR

This paper investigates the maximum number of zeros at 1 for polynomials with degree at most n and constrained coefficients, extending known inequalities and establishing sharp bounds with connections to Coppersmith-Rivlin inequalities.

Contribution

It extends the Coppersmith-Rivlin inequality to provide sharp bounds on the zeros at 1 for polynomials with coefficient constraints.

Findings

Established sharp bounds on zeros at 1 for constrained polynomials

Extended the Coppersmith-Rivlin inequality to new polynomial classes

Connected polynomial zero bounds to inequality extensions

Abstract

We examine the maximal number of zeros a polynomial of degree at most n with constrained coefficients may have at 1. Our results are essentially sharp and extend earlier results of this variety. An interesting connection to certain extensions of the Coppersmith-Rivlin inequality is explored.