Mahler Measure of "Almost" Reciprocal Polynomials

TL;DR

This paper establishes a lower bound for the Mahler measure of polynomials that are nearly reciprocal, where the outer coefficients mirror each other but the inner ones do not, expanding understanding of polynomial measures.

Contribution

It introduces a lower bound for the Mahler measure on a new class of 'almost' reciprocal polynomials, extending previous results on reciprocal polynomials.

Findings

Lower bound for Mahler measure of 'almost' reciprocal polynomials

Characterization of coefficient symmetry in polynomial measures

Extension of Mahler measure bounds to near-reciprocal cases

Abstract

Here we give a lower bound of the Mahler measure on a set of polynomials that are "almost" reciprocal. Here "almost" reciprocal means that the outermost coefficients of each polynomial mirror each other in proportion, while this pattern breaks down for the innermost coefficients.