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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The cyclotomic numbers of order seven


Authors: Philip A. Leonard and Kenneth S. Williams
Journal: Proc. Amer. Math. Soc. 51 (1975), 295-300
MSC: Primary 12C20; Secondary 10A40
MathSciNet review: 0371868
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Abstract: The cyclotomic numbers of order seven are given in terms of the solutions of a certain system of three quadratic diophantine equations. This is analogous to L. E. Dickson's evaluation of the cyclotomic numbers of order five, and is a convenient approach for applications to the theory of power residues.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1975-0371868-8
PII: S 0002-9939(1975)0371868-8
Keywords: Cyclotomic numbers, Jacobi sums, Dickson-Hurwitz sums
Article copyright: © Copyright 1975 American Mathematical Society