Large Sieve Inequalities via Subharmonic Methods and the Mahler Measure of the Fekete Polynomials

Sieve-type Lower Bounds for the Mahler Measure of Polynomials on Subarcs

We prove sieve-type lower bounds for the Mahler measure of polynomials on subarcs of the unit circle of the complex plane. This is then applied to give an essentially sharp lower bound for the Mahler measure of the Fekete polynomials on subarcs.

Lower Bounds for the Mahler Measure of Polynomials on Subarcs

We give lower bounds for the Mahler measure of polynomials with constrained coefficients, including Littlewood polynomials, on subarcs of the unit circle of the complex plane. This is then applied to give an essentially sharp lower bound for the Mahler measure of the Fekete polynomials on subarcs.

Polynomials with small Mahler measure

We describe several searches for polynomials with integer coefficients and small Mahler measure. We describe the algorithm used to test Mahler measures. We determine all polynomials with degree at most 24 and Mahler measure less than 1.3, test all reciprocal and antireciprocal polynomials with height 1 and degree at most 40, and check certain sparse polynomials with height 1 and degree as large...

The Fekete-Szego Coefficient Functional for Transforms of Analytic Functions

Weighted inequalities for generalized polynomials with doubling weights

Many weighted polynomial inequalities, such as the Bernstein, Marcinkiewicz, Schur, Remez, Nikolskii inequalities, with doubling weights were proved by Mastroianni and Totik for the case [Formula: see text], and by Tamás Erdélyi for [Formula: see text]. In this paper we extend such polynomial inequalities to those for generalized trigonometric polynomials. We also prove the large sieve for gene...