Note on the Cyclotomic Polynomial

1954 ◽  
Vol 61 (2) ◽  
pp. 106
Author(s):  
L. Carlitz
Keyword(s):  
Cyclotomic Polynomial

scholarly journals On the magnitude of the coefficients of the cyclotomic polynomial

1936 ◽  
Vol 42 (6) ◽  
pp. 389-393 ◽  
Author(s):  
Emma Lehmer
Keyword(s):  
Cyclotomic Polynomial

scholarly journals Some q-supercongruences modulo the fourth power of a cyclotomic polynomial

2021 ◽  
Vol 182 ◽  
pp. 105469
Author(s):  
Chuanan Wei
Keyword(s):  
Cyclotomic Polynomial ◽  
Fourth Power

scholarly journals The order of magnitude of the mth coefficients of cyclotomic polynomials

1985 ◽  
Vol 27 ◽  
pp. 143-159 ◽  
Author(s):  
H. L. Montgomery ◽  
R. C. Vaughan
Keyword(s):  
Cyclotomic Polynomial ◽  
Cyclotomic Polynomials ◽  
Order Of Magnitude ◽  
Euler’S Function ◽  
Image Position

We define the nth cyclotomic polynomial Φn(z) by the equationand we writewhere ϕ is Euler's function.Erdös and Vaughan [3] have shown thatuniformly in n as m-→∞, whereand that for every large m

scholarly journals On the coefficients of the cyclotomic polynomial

1946 ◽  
Vol 52 (2) ◽  
pp. 179-185 ◽  
Author(s):  
Paul Erdös
Keyword(s):  
Cyclotomic Polynomial

The Number of Terms in the Cyclotomic Polynomial F pq (x)

1966 ◽  
Vol 73 (9) ◽  
pp. 979 ◽  
Author(s):  
L. Carlitz
Keyword(s):  
Cyclotomic Polynomial

Magnitude of the coefficients of the cyclotomic polynomial $F\sb{pqr}$ , II

1971 ◽  
Vol 38 (3) ◽  
pp. 591-594 ◽  
Author(s):  
Marion Beiter
Keyword(s):  
Cyclotomic Polynomial

scholarly journals The cyclotomic polynomial topologically

2014 ◽  
Vol 2014 (687) ◽  
Author(s):  
Gregg Musiker ◽  
Victor Reiner
Keyword(s):  
Cyclotomic Polynomial ◽  
Simplicial Homology

Abstract.We interpret the coefficients of the cyclotomic polynomial in terms of simplicial homology.

scholarly journals On Mixed Almost Moore Graphs of Diameter Two

10.37236/5647 ◽  
2016 ◽  
Vol 23 (2) ◽  
Author(s):  
Nacho López ◽  
Josep M. Miret
Keyword(s):  
Characteristic Polynomial ◽  
Necessary Conditions ◽  
Directed Graphs ◽  
Cyclotomic Polynomial ◽  
Mixed Case ◽  
Mixed Graphs

Mixed almost Moore graphs appear in the context of the Degree/Diameter problem as a class of extremal mixed graphs, in the sense that their order is one less than the Moore bound for mixed graphs. The problem of their existence has been considered before for directed graphs and undirected ones, but not for the mixed case, which is a kind of generalization. In this paper we give some necessary conditions for the existence of mixed almost Moore graphs of diameter two derived from the factorization in $\mathbb{Q}[x]$ of their characteristic polynomial. In this context, we deal with the irreducibility of $\Phi_i(x^2+x-(r-1))$, where $\Phi_i(x)$ denotes the i-th cyclotomic polynomial.

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