Sparse binary cyclotomic polynomials

TL;DR

This paper investigates the sparsity of binary cyclotomic polynomials, establishing bounds on how many have a limited number of nonzero terms relative to their degree.

Contribution

It provides new bounds on the count of binary cyclotomic polynomials with a restricted number of nonzero terms, advancing understanding of their structural properties.

Findings

Derived bounds for the number of sparse binary cyclotomic polynomials

Established relationships between polynomial sparsity and degree

Enhanced theoretical understanding of cyclotomic polynomial distributions

Abstract

We derive a lower and an upper bound for the number of binary cyclotomic polynomials $\Phi_m$ with at most $m^{1/2+\epsilon}$ nonzero terms.