Connection between Gaussian periods and cyclic units

Emma Lehmer
1988 Mathematics of Computation  
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* + 5n3 + 15n2 + 25n + 25.
doi:10.1090/s0025-5718-1988-0929551-0 fatcat:zceyd4jybfh5zoekvrb4j6rre4