Cyclotomic coefficients: gaps and jumps

TL;DR

This paper advances the understanding of cyclotomic polynomial coefficients by improving existing results on gaps and jumps, introducing novel techniques, and providing deeper insights into their behavior.

Contribution

It offers new bounds and methods for analyzing gaps and jumps in cyclotomic polynomial coefficients, surpassing previous results.

Findings

Improved bounds on gaps and jumps in cyclotomic coefficients

Introduction of new analytical techniques for coefficient analysis

Enhanced understanding of coefficient distribution patterns

Abstract

We improve several recent results by Hong, Lee, Lee and Park (2012) on gaps and Bzd\c{e}ga (2014) on jumps amongst the coefficients of cyclotomic polynomials. Besides direct improvements, we also introduce several new techniques that have never been used in this area.