Connection between Gaussian periods and cyclic units

Lehmer, Emma

doi:10.1090/S0025-5718-1988-0929551-0

Connection between Gaussian periods and cyclic units
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Math. Comp. 50 (1988), 535-541 Request permission

Abstract:

This paper finds that all known parametric families of units in real quadratic, cubic, quartic and sextic fields with prime conductor are linear combinations of Gaussian periods and exhibits these combinations. This approach is used to find new units in the real quintic field for prime conductors $p = {n^4} + 5{n^3} + 15{n^2} + 25n + 25$

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Publ. Math. Besançon

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