Bounds on ternary cyclotomic coefficients

TL;DR

This paper establishes new bounds on the maximum absolute value of coefficients in ternary cyclotomic polynomials and proves that consecutive coefficients differ by at most one, advancing understanding of their structure.

Contribution

It introduces a novel bound on the maximum coefficient magnitude and proves a new property about the difference between consecutive coefficients.

Findings

New upper bound on |a_{pqr}(n)|

Consecutive coefficients differ by at most one

Enhanced understanding of ternary cyclotomic polynomial structure

Abstract

We present a new bound on $A = \max_n |a_{pqr}(n)|$, where $a_{pqr}(n)$ are the coefficients of a ternary cyclotomic polynomial. We also prove that two consecutive coefficients of such a polynomial differ by at most one.