Cyclotomy and delta units

Lazarus, Andrew J.

doi:10.1090/S0025-5718-1993-1189520-7

Cyclotomy and delta units
HTML articles powered by AMS MathViewer

by Andrew J. Lazarus PDF

Math. Comp. 61 (1993), 295-305 Request permission

Abstract:

In this paper we examine cyclic cubic, quartic, and quintic number fields of prime conductor p containing units that bear a special relationship to the classical Gaussian periods: ${\eta _j} - {\eta _{j + 1}} + c$ is a unit for periods ${\eta _j}$ and $c \in \mathbb {Z}$.

References

Die Lehre von der Kreisteilung

L. E. Dickson, Cyclotomy, Higher Congruences, and Waring’s Problem, Amer. J. Math. 57 (1935), no. 2, 391–424. MR 1507083, DOI 10.2307/2371217

Table numérique du nombre de classes et des unités des extensions cycliques de degré

de

Arithmetische Bestimmung von Grundeinheit und Klassenzahl in zyklischen kubischen und biquadratischen Zahlkörpern

S. A. Katre and A. R. Rajwade, Complete solution of the cyclotomic problem in $\textbf {F}_q$ for any prime modulus $l,\;q=p^\alpha ,\;p\equiv 1\;(\textrm {mod}\,l)$, Acta Arith. 45 (1985), no. 3, 183–199. MR 808019, DOI 10.4064/aa-45-3-183-199
S. A. Katre and A. R. Rajwade, Unique determination of cyclotomic numbers of order five, Manuscripta Math. 53 (1985), no. 1-2, 65–75. MR 804338, DOI 10.1007/BF01174011
S. A. Katre and A. R. Rajwade, Resolution of the sign ambiguity in the determination of the cyclotomic numbers of order $4$ and the corresponding Jacobsthal sum, Math. Scand. 60 (1987), no. 1, 52–62. MR 908829, DOI 10.7146/math.scand.a-12171
Andrew J. Lazarus, Gaussian periods and units in certain cyclic fields, Proc. Amer. Math. Soc. 115 (1992), no. 4, 961–968. MR 1093600, DOI 10.1090/S0002-9939-1992-1093600-5
D. H. Lehmer and Emma Lehmer, The Lehmer project, Math. Comp. 61 (1993), no. 203, 313–317. MR 1189521, DOI 10.1090/S0025-5718-1993-1189521-9
Emma Lehmer, Connection between Gaussian periods and cyclic units, Math. Comp. 50 (1988), no. 182, 535–541. MR 929551, DOI 10.1090/S0025-5718-1988-0929551-0
Emma Lehmer, Connection between Gaussian periods and cyclic units, Math. Comp. 50 (1988), no. 182, 535–541. MR 929551, DOI 10.1090/S0025-5718-1988-0929551-0
Daniel Shanks, The simplest cubic fields, Math. Comp. 28 (1974), 1137–1152. MR 352049, DOI 10.1090/S0025-5718-1974-0352049-8
Thomas Storer, Cyclotomy and difference sets, Lectures in Advanced Mathematics, No. 2, Markham Publishing Co., Chicago, Ill., 1967. MR 0217033