Value distribution of cyclotomic polynomial coefficients
Abstract
Let a_n(k) be the kth coefficient of the nth cyclotomic polynomial Phi_n(x). As n ranges over the integers, a_n(k) assumes only finitely many values. For any such value v we determine the density of integers n such that a_n(k)=v. Also we study the average of the a_n(k). We derive analogous results for the kth Taylor coefficient of 1/Phi_n(x) (taken around x=0), the kth coefficient of the nth reciprocal cyclotomic polynomial. We formulate various open problems.
Keywords
Cite
@article{arxiv.0803.2483,
title = {Value distribution of cyclotomic polynomial coefficients},
author = {Yves Gallot and Pieter Moree and Huib Hommersom},
journal= {arXiv preprint arXiv:0803.2483},
year = {2012}
}
Comments
26 pages, 6 tables. Partly based on arXiv:math.NT/0307352, which is the M.Sc. thesis of H. Hommersom (2003), enriched with research results due to Moree. Some of these research results have been extracted and various new results added. A connection with reciprocal cyclotomic polynomials (arXiv:0709.1570) is also made