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Swinnerton-Dyer Polynomial

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The minimal polynomial S_n(x) whose roots are sums and differences of the square roots of the first n primes,

S_n(x)=product(x+/-sqrt(2)+/-sqrt(3)+/-sqrt(5)+/-...+/-sqrt(p_n)).
(1)

The first few Swinnerton-Dyer polynomials are

S_1(x)=x^2-2
(2)
S_2(x)=x^4-10x^2+1
(3)
S_3(x)=x^8-40x^6+352x^4-960x^2+576.
(4)

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References

Sloane, N. J. A. Sequences A153731 in "The On-Line Encyclopedia of Integer Sequences."Vardi, I. Computational Recreations in Mathematica. Redwood City, CA: Addison-Wesley, pp. 11 and 225-226, 1991.

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Swinnerton-Dyer Polynomial

Cite this as:

Weisstein, Eric W. "Swinnerton-Dyer Polynomial." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Swinnerton-DyerPolynomial.html

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