The Coefficients of Cyclotomic Polynomials

1990 ◽  
pp. 349-366 ◽  
Author(s):  
Helmut Maier
Keyword(s):  
Cyclotomic Polynomials

A Note on Golomb's “Cyclotomic Polynomials and Factorization Theorems”

1981 ◽  
Vol 88 (10) ◽  
pp. 753-753
Author(s):  
Katherine E. McLain ◽  
Hugh M. Edgar
Keyword(s):  
Cyclotomic Polynomials

scholarly journals On multiple prime divisors of cyclotomic polynomials

1974 ◽  
Vol 28 (127) ◽  
pp. 847-847 ◽  
Author(s):  
Wayne L. McDaniel
Keyword(s):  
Cyclotomic Polynomials ◽  
Prime Divisors

scholarly journals On modular inverses of cyclotomic polynomials and the magnitude of their coefficients

2012 ◽  
Vol 15 ◽  
pp. 44-58 ◽  
Author(s):  
Clément Dunand
Keyword(s):  
Upper Bounds ◽  
Cyclotomic Polynomials ◽  
Lower And Upper Bounds

AbstractLet p and r be two primes, and let n and m be two distinct divisors of pr. Consider Φn and Φm, the nth and mth cyclotomic polynomials. In this paper, we present lower and upper bounds for the coefficients of the inverse of Φn modulo Φm and discuss an application to torus-based cryptography.

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

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