Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



The octic periodic polynomial

Author: Ronald J. Evans
Journal: Proc. Amer. Math. Soc. 87 (1983), 389-393
MSC: Primary 10G05
MathSciNet review: 684624
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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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Keywords: Octic period polynomial
Article copyright: © Copyright 1983 American Mathematical Society