On the coefficients of the cyclotomic polynomials of order three
Number Theory
2009-10-13 v1
Abstract
We say that a cyclotomic polynomial Phi_{n}(x) has order three if n is the product of three distinct primes, p<q<r. Let A(n) be the largest absolute value of a coefficient of Phi_{n}(x) and M(p) be the maximum of A(pqr). In 1968, Sister Marion Beiter conjectured that A(pqr)<=(p+1)/2. In 2008, Yves Gallot and Pieter Moree showed that the conjecture is false for every p>=11, and they proposed the Corrected Beiter conjecture: M(p)<=2p/3. Here we will give a sufficient condition for the Corrected Beiter conjecture and prove it when p=7.
Cite
@article{arxiv.0910.1982,
title = {On the coefficients of the cyclotomic polynomials of order three},
author = {Jia Zhao and Xianke Zhang},
journal= {arXiv preprint arXiv:0910.1982},
year = {2009}
}
Comments
16pages, submitted to J. Number Theory