A survey on coefficients of cyclotomic polynomials
C Sanna - Expositiones Mathematicae, 2022 - Elsevier
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 …
study has a very long history, which goes back at least to Gauss (1801). In particular, the …
Calculating cyclotomic polynomials
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 first algorithm calculates $\Phi _n (z) $ by a series of polynomial divisions, which we …
The story of algebraic numbers in the first half of the 20th century
W Narkiewicz - Springer Monographs in Mathematics. Springer, Cham, 2018 - Springer
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 …
achieved in the first half of the twentieth century and may be viewed as a companion to my …
Flat cyclotomic polynomials: a new approach
S Elder - arXiv preprint arXiv:1207.5811, 2012 - arxiv.org
We build a new theory for analyzing the coefficients of any cyclotomic polynomial by
considering it as a gcd of simpler polynomials. Using this theory, we generalize a result …
considering it as a gcd of simpler polynomials. Using this theory, we generalize a result …
A Note on Heights of Cyclotomic Polynomials
G Bachman, C Bao, S Wu - arXiv preprint arXiv:2309.03422, 2023 - arxiv.org
arXiv:2309.03422v1 [math.NT] 7 Sep 2023 Page 1 arXiv:2309.03422v1 [math.NT] 7 Sep 2023
A NOTE ON HEIGHTS OF CYCLOTOMIC POLYNOMIALS GENNADY BACHMAN …
A NOTE ON HEIGHTS OF CYCLOTOMIC POLYNOMIALS GENNADY BACHMAN …
Maximum gap in cyclotomic polynomials
M Ambrosino, H Hong, E Lee - Journal of Number Theory, 2021 - Elsevier
We study the maximum gap g (maximum of the differences between any two consecutive
exponents) of cyclotomic polynomials. In 2012, Hong, Lee, Lee and Park showed that g (Φ p …
exponents) of cyclotomic polynomials. In 2012, Hong, Lee, Lee and Park showed that g (Φ p …
Bounds for the maximal height of divisors of xn− 1
N Kaplan - Journal of Number Theory, 2009 - Elsevier
TEXT: The problem of determining the maximum size of coefficients of cyclotomic
polynomials has been studied extensively. Let A (n) be the maximum absolute value of a …
polynomials has been studied extensively. Let A (n) be the maximum absolute value of a …
[PDF][PDF] Structures and Properties of Cyclotomic Polynomials.
AQM Al-Kateeb - 2016 - repository.lib.ncsu.edu
ABSTRACT AL-KATEEB, ALA'A QASEM MOHAMMAD. Structures and Properties of
Cyclotomic Polynomials.(Under the direction of Hoon Hong.) The cyclotomic polynomial Φn …
Cyclotomic Polynomials.(Under the direction of Hoon Hong.) The cyclotomic polynomial Φn …
Constrained ternary integers
An integer n is said to be ternary if it is composed of three distinct odd primes. In this paper,
we asymptotically count the number of ternary integers n≤ x with the constituent primes …
we asymptotically count the number of ternary integers n≤ x with the constituent primes …
On the number of terms of some families of the ternary cyclotomic polynomials Φ3p2p3
A Al-Kateeb, A Dagher - Rad Hrvatske akademije znanosti i umjetnosti …, 2023 - hrcak.srce.hr
ON THE NUMBER OF TERMS OF SOME FAMILIES OF THE TERNARY CYCLOTOMIC
POLYNOMIALS Φ3p2p3 Ala’a Al-Kateeb and Afnan Dagher 1. Intr Page 1 RAD HAZU …
POLYNOMIALS Φ3p2p3 Ala’a Al-Kateeb and Afnan Dagher 1. Intr Page 1 RAD HAZU …