The octic periodic polynomial

Evans, Ronald J.

doi:10.1090/S0002-9939-1983-0684624-2

The octic periodic polynomial
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Proc. Amer. Math. Soc. 87 (1983), 389-393 Request permission

Abstract:

The coefficients and the discriminant of the octic period polynomial ${\psi _8}(z)$ are computed, where, for a prime $p = 8f + 1$, ${\psi _8}(z)$ denotes the minimal polynomial over ${\mathbf {Q}}$ of the period $(1/8)\sum \nolimits _{n = 1}^{p - 1} {\exp (2\pi i{n^8}/p)}$. Also, the finite set of prime octic nonresidues $(\mod p)$ which divide integers represented by ${\psi _8}(z)$ is characterized.

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On the multisection of the roots of unity

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