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

 

Gaussian periods and units in certain cyclic fields


Author: Andrew J. Lazarus
Journal: Proc. Amer. Math. Soc. 115 (1992), 961-968
MSC: Primary 11R16; Secondary 11L05, 11R27
MathSciNet review: 1093600
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Abstract: We analyze the property of period-unit integer translation (there exists a Gaussian period $ \eta $ and rational integer $ c$ such that $ \eta + c$ is a unit) in simplest quadratic, cubic, and quartic fields of arbitrary conductor. This is an extension of work of E. Lehmer, R. Schoof, and L. C. Washington for prime conductor. We also determine the Gaussian period polynomial for arbitrary conductor.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1992-1093600-5
PII: S 0002-9939(1992)1093600-5
Keywords: Gaussian period, period polynomial, simplest fields, units
Article copyright: © Copyright 1992 American Mathematical Society