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The octic periodic polynomial


Author: Ronald J. Evans
Journal: Proc. Amer. Math. Soc. 87 (1983), 389-393
MSC: Primary 10G05
DOI: https://doi.org/10.1090/S0002-9939-1983-0684624-2
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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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1983-0684624-2
Keywords: Octic period polynomial
Article copyright: © Copyright 1983 American Mathematical Society

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