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 …

Given a numerical semigroup S, we let \mathrmP_S(x)=(1-x)s∈Sx^s be its semigroup
polynomial. We study cyclotomic numerical semigroups; these are numerical semigroups S …

Let $ A_n $ denote the height of cyclotomic polynomial $\Phi_n $, where $ n $ is a product of
$ k $ distinct odd primes. We prove that $ A_n\le\epsilon_k\phi (n)^{k^{-1} 2^{k-1}-1} $ with …

We gather together several bounds on the sizes of coefficients which can appear in factors
of polynomials in Z [x]; we include a new bound which was latent in a paper by Mignotte, and …

ABSTRACT AL-KATEEB, ALA'A QASEM MOHAMMAD. Structures and Properties of
Cyclotomic Polynomials.(Under the direction of Hoon Hong.) The cyclotomic polynomial Φn …

In this paper, we list several interesting structures of cyclotomic polynomials: specifically
relations among blocks obtained by suitable partition of cyclotomic polynomials. We present …

We say a polynomial f having integer coefficients is strongly coefficient convex if the set of
coefficients of f consists of consecutive integers only. We establish various results …

Some conjectures on the maximal heightof divisors of xn-1 Page 1 a journal of mathematics
msp Some conjectures on the maximal height of divisors of xn −1 Nathan C. Ryan, Bryan C …

The height of a polynomial f (x) is the largest coefficient of f (x) in absolute value. Let B (n) be
the largest height of a polynomial in ℤ [x] dividing xn-1. In this paper, we investigate the …

Let a (r, n) be rth coefficient of nth cyclotomic polynomial. Suzuki proved that {a (r, n)| r≥ 1,
n≥ 1}= Z. If m and n are two natural numbers we prove an analogue of Suzuki's theorem for …