S000428


The Bombieri norm of Phi(n,x), the n-th cyclotomic polynomial.

1, 2, 2, 4, 2, 16, 4, 64, 2, 22, 16, 1024, 8, 4096, 64, 200, 2, 65536, 22, 262144, 128, 2380, 1024, 4194304, 72, 215766, 4096, 48622, 2048, 268435456, 200, 1073741824, 2, 765248, 65536, 14136356, 926, 68719476736, 262144, 10228426, 16512, 1099511627776, 2380

0

S000428

Note that the norm is 2 for all n = 2^k with k >= 0. When n is prime then the term is 2^(n-1).

T. D. Noe, Plot of 1025 terms

T. D. Noe, Table of 1025 terms

Eric W. Weinstein, MathWorld: Bombieri Norm

(Mma) Table[c = CoefficientList[Cyclotomic[n, x], x]; deg = Length[c] - 1; Binomial[deg, Range[0, deg]].Abs[c], {n, 0, 50}]

Cf. A051664A160338, S000426S000427.

nonn,nice

T. D. Noe, Dec 19 2014

© Tony D Noe 2014-2015