Gaussian periods and units in certain cyclic fields

Lazarus, Andrew J.

doi:10.1090/S0002-9939-1992-1093600-5

Gaussian periods and units in certain cyclic fields
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Proc. Amer. Math. Soc. 115 (1992), 961-968 Request permission

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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