Cyclotomy and delta units
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- 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
-
Paul Bachmann, Die Lehre von der Kreisteilung, Teubner, Leipzig and Berlin, 1927.
- 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 Marie-Nicole Gras, Table numérique du nombre de classes et des unités des extensions cycliques de degré 4 de $\mathbb {Q}$, Publ. Math. Fasc. 2, Fac. Sci. Besançon, 1977/1978. Helmut Hasse, Arithmetische Bestimmung von Grundeinheit und Klassenzahl in zyklischen kubischen und biquadratischen Zahlkörpern, Math. Abhandlungen, vol. 3, Walter deGruyter, Berlin, 1975, pp. 285-379; originally published 1950.
- 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
Additional Information
- © Copyright 1993 American Mathematical Society
- Journal: Math. Comp. 61 (1993), 295-305
- MSC: Primary 11R27; Secondary 11R16, 11R18, 11R20
- DOI: https://doi.org/10.1090/S0025-5718-1993-1189520-7
- MathSciNet review: 1189520