Maximal height of divisors of $x\sp n-1$
Pomerance, Carl ; Ryan, Nathan C.
Illinois J. Math., Tome 51 (2007) no. 3, p. 597-604 / Harvested from Project Euclid
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The size of the coefficients of cyclotomic polynomials is a problem that has been well-studied. This paper investigates the following generalization: suppose $f(x)\in\mathbb{Z}[x]$ is a divisor of $x^n-1$, so that $f(x)$ is the product of the cyclotomic polynomials corresponding to some of the divisors of $n$. We ask about the largest coefficient in absolute value over all such divisors $f(x)$ of $x^n-1$, obtaining a fairly tight estimate for the maximal order of this function.
Publié le : 2007-04-15
Classification:  12Y05,  11C08,  11Y70,  13B25 
@article{1258138432,
     author = {Pomerance, Carl and Ryan, Nathan C.},
     title = {Maximal height of divisors of $x\sp n-1$},
     journal = {Illinois J. Math.},
     volume = {51},
     number = {3},
     year = {2007},
     pages = { 597-604},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1258138432}
}

Pomerance, Carl; Ryan, Nathan C. Maximal height of divisors of $x\sp n-1$. Illinois J. Math., Tome 51 (2007) no. 3, pp.  597-604. http://gdmltest.u-ga.fr/item/1258138432/