The lowest degree 0,1-polynomial divisible by cyclotomic polynomial

2011/06/07 by A. Satyanarayana Reddy, Reddy, A. Satyanarayana
Mathematics · #11C08 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11C08

paper · pdf · doi:10.48550/arxiv.1106.1271

7 pages

arxiv created 2011/11/15 · arxiv updated 2011/11/16

Abstract

Let n be an even positive integer with at most three distinct prime factors and let \ze_n be a primitive n-th root of unity. In this study, we made an attempt to find the lowest-degree 0,1-polynomial f(x) ∈ \Q[x] having at least three terms such that f(\ze_n) is a minimal vanishing sum of the n-th roots of unity.

Related

• The lowest-degree polynomials with non-negative coefficients
• The Schur polynomials in all primitive nth roots of unity
• Binary polynomial power sums vanishing at roots of unity
• Classifying minimal vanishing sums of roots of unity
• On the irreducibility of the non-cyclotomic part of most 0,1-polynomials with few terms