Cyclotomic polynomials play an important role in several areas of mathematics and their
study has a very long history, which goes back at least to Gauss (1801). In particular, the …

We present three algorithms to calculate $\Phi _n (z) $, the $ n_ {th} $ cyclotomic polynomial.
The first algorithm calculates $\Phi _n (z) $ by a series of polynomial divisions, which we …

The nth cyclotomic polynomial Φ n (x) is the minimal polynomial of an nth primitive root of
unity. Its coefficients are the subject of intensive study and some formulas are known for …

Let Φ n (x) denote the n th cyclotomic polynomial. In 1968 Sister Marion Beiter conjectured
that an (k), the coefficient of xk in Φ n (x), satisfies| an (k)|≦(p+ 1)/2 in case n= pqr with p< q< …

Given any positive integer n, let A (n) denote the height of the n th cyclotomic polynomial,
that is its maximum coefficient in absolute value. It is well known that A (n) is unbounded. We …

A cyclotomic polynomial Phi_n (x) is said to be ternary if n= pqr with p, q and r distinct odd
prime factors. Ternary cyclotomic polynomials are the simplest ones for which the behaviour …

It is customary to define a cyclotomic polynomial Φn (x) to be ternary if n is the product of
three distinct primes, p< q< r. Let A (n) be the largest absolute value of a coefficient of Φn (x) …

The aim of this book is to give a survey of results in the theory of algebraic numbers
achieved in the first half of the twentieth century and may be viewed as a companion to my …

In this article we prove a result about sets of coefficients of cyclotomic polynomials. We then
give corollaries related to flat cyclotomic polynomials and establish the first known infinite …

Remarks on the flatness of ternary cyclotomic polynomials Page 1 International Journal of
Number Theory Vol. 13, No. 2 (2017) 529–547 c World Scientific Publishing Company DOI …