Swinnerton - Dyer Polynomial

Author

Eric W. Weisstein
December 31, 2008

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Algebra/Swinnerton-DyerPolynomial.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/Swinnerton-DyerPolynomial.html.

©2008 Wolfram Research, Inc. except for portions noted otherwise

Polynomial

SwinnertonDyer[n_,x_]:=Times@@((x+Total[#])&/@Flatten[Outer[List,Sequence@@Outer[Times,Sqrt[Prime[Range[n]]],{-1,1}]],n-1])

With[{n=3},Flatten[Outer[List,Sequence@@Outer[Times,Sqrt[Prime[Range[n]]],{-1,1}]],n-1]]

Table[SwinnertonDyer[n,x]//Expand,{n,4}]//Column//TraditionalForm

CoefficientList[#,x^2]&/@Table[SwinnertonDyer[n,x]//Expand,{n,4}]