Shanks, Daniel The simplest cubic fields. (English) Zbl 0307.12005 Math. Comput. 28, 1137-1152 (1974). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 12 ReviewsCited in 87 Documents MSC: 11R16 Cubic and quartic extensions 11R18 Cyclotomic extensions 11R23 Iwasawa theory 11R42 Zeta functions and \(L\)-functions of number fields 11R80 Totally real fields × Cite Format Result Cite Review PDF Full Text: DOI References: [1] H. J. Godwin and P. A. Samet, A table of real cubic fields, J. London Math. Soc. 34 (1959), 108 – 110. · Zbl 0085.02603 · doi:10.1112/jlms/s1-34.1.108 [2] H. J. Godwin, The determination of the class-numbers of totally real cubic fields., Proc. Cambridge Philos. Soc. 57 (1961), 728 – 730. · Zbl 0106.02804 [3] A. I. Borevich and I. R. Shafarevich, Number theory, Translated from the Russian by Newcomb Greenleaf. Pure and Applied Mathematics, Vol. 20, Academic Press, New York-London, 1966. · Zbl 0145.04902 [4] H. J. Godwin, The determination of units in totally real cubic fields, Proc. Cambridge Philos. Soc. 56 (1960), 318 – 321. · Zbl 0116.02802 [5] Carol Neild and Daniel Shanks, On the 3-rank of quadratic fields and the Euler product, Math. Comp. 28 (1974), 279 – 291. · Zbl 0277.12005 [6] Daniel Shanks, On the conjecture of Hardy & Littlewood concerning the number of primes of the form \?²+\?, Math. Comp. 14 (1960), 320 – 332. · Zbl 0098.03705 [7] Daniel Shanks and Peter Weinberger, A quadratic field of prime discriminant requiring three generators for its class group, and related theory, Acta Arith. 21 (1972), 71 – 87. · Zbl 0249.12010 [8] B. D. Beach, H. C. Williams, and C. R. Zarnke, Some computer results on units in quadratic and cubic fields, Proceedings of the Twenty-Fifth Summer Meeting of the Canadian Mathematical Congress (Lakehead Univ., Thunder Bay, Ont., 1971) Lakehead Univ., Thunder Bay, Ont., 1971, pp. 609 – 648. · Zbl 0348.12003 [9] FRANK GERTH III, Sylow 3-Subgroups of Ideal Class Groups of Certain Cubic Fields, Thesis, Princeton University, Princeton, N. J., 1972. · Zbl 0268.12001 [10] GEORGE GRAS, Sur les l-Classes d’Idéaux dans les Extensions Cycliques Relative de Degré Premier l, Thesis, Grenoble, 1972. [11] Pierre Barrucand and Harvey Cohn, A rational genus, class number divisibility, and unit theory for pure cubic fields, J. Number Theory 2 (1970), 7 – 21. · Zbl 0192.40001 · doi:10.1016/0022-314X(70)90003-X [12] Pierre Barrucand and Harvey Cohn, Remarks on principal factors in a relative cubic field, J. Number Theory 3 (1971), 226 – 239. · Zbl 0218.12002 · doi:10.1016/0022-314X(71)90040-0 [13] Daniel Shanks and Larry P. Schmid, Variations on a theorem of Landau. I, Math. Comp. 20 (1966), 551 – 569. · Zbl 0156.05104 [14] Morris Newman, A table of the first factor for prime cyclotomic fields, Math. Comp. 24 (1970), 215 – 219. · Zbl 0198.36902 [15] Heinrich W. Leopoldt, Zur Geschlechtertheorie in abelschen Zahlkörpern, Math. Nachr. 9 (1953), 351 – 362 (German). · Zbl 0053.35502 · doi:10.1002/mana.19530090604 [16] M. N. Gras, N. Moser, and J. J. Payan, Approximation algorithmique du groupe des classes de certains corps cubiques cycliques, Acta Arith. 23 (1973), 295 – 300 (French). · Zbl 0232.12002 [17] Helmut Hasse, Arithmetische Bestimmung von Grundeinheit und Klassenzahl in zyklischen kubischen und biquadratischen Zahlkörpern, Abh. Deutsch. Akad. Wiss. Berlin. Math.-Nat. Kl. 1948 (1948), no. 2, 95 pp. (1950) (German). · Zbl 0035.30502 [18] MARIE-NICOLE MONTOUCHET, Sur le Nombre de Classes du Sous-Corps Cubique de \( {Q^{(p)}}(p \equiv 1(3))\), Thesis, Grenoble, 1971. · Zbl 0244.12005 [19] Marie-Nicole Gras, Méthodes et algorithmes pour le calcul numérique du nombre de classes et des unités des extensions cubiques cycliques de \?, J. Reine Angew. Math. 277 (1975), 89 – 116 (French). · Zbl 0315.12007 · doi:10.1515/crll.1975.277.89 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.