Lenstra, H. W. jun. Euclidean number fields of large degree. (English) Zbl 0328.12007 Invent. Math. 38, 237-254 (1977). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 6 ReviewsCited in 25 Documents MSC: 11R27 Units and factorization 13F10 Principal ideal rings 52C17 Packing and covering in \(n\) dimensions (aspects of discrete geometry) 12J10 Valued fields PDF BibTeX XML Cite \textit{H. W. Lenstra jun.}, Invent. Math. 38, 237--254 (1977; Zbl 0328.12007) Full Text: DOI EuDML OpenURL References: [1] Biedermann, D., Richter, W.: Minimaldiskriminanten von primitiven Zahlkörpern sechsten Grades im totalreellen und totalkomplexen Fall. Universität Karlsruhe, 1974 · Zbl 0293.12005 [2] Cartier, P., Roy, Y.: On the enumeration of quintic fields with small discriminant. J. Reine Angew. Math.268/269, 213-215 (1974) · Zbl 0285.12001 [3] Cassels, J.W.S.: The inhomogeneous minimum of binary quadratic, ternary cubic and quaternary quartic forms. Proc. Cambridge Philos. Soc.48, 72-86, 519-520 (1952) · Zbl 0046.04601 [4] Chowla, S.: Proof of a conjecture of Julia Robinson. Norske Vid. Selsk. Forh. (Trondheim)34, 100-101 (1961) · Zbl 0105.02803 [5] Cohn, H.: A numerical study of quintics of small discriminant. Comm. Pure Appl. Math.8, 377-385 (1955) · Zbl 0065.03001 [6] Godwin, H.J.: Real quartic fields with small discriminant. J. London Math. Soc.31, 478-485 (1956) · Zbl 0071.03401 [7] Godwin, H.J.: On totally complex quartic fields with small discriminants. Proc. Cambridge Philos. Soc.53, 1-4 (1957) · Zbl 0077.04601 [8] Godwin, H.J.: On quartic fields of signature one with small discriminant. Quart. J. Math. Oxford Ser.8, 214-222 (1957) · Zbl 0079.05704 [9] Godwin, H.J.: On the inhomogeneous minima of totally real cubic norm-forms. J. London Math. Soc.40, 623-627 (1965) · Zbl 0132.28204 [10] Godwin, H.J.: On Euclid’s algorithm in some quartic and quintic fields. J. London Math. Soc.40, 699-704 (1965) · Zbl 0132.28301 [11] Godwin, H.J.: On Euclid’s algorithm in some cubic fields with signature one. Quart. J. Math. Oxford Ser.18, 333-338 (1967) · Zbl 0159.07201 [12] Györy, K.: Sur les polynômes à coefficients entiers et de discriminant donné, II. Publ. Math. Debrecen21, 125-144 (1974) · Zbl 0303.12001 [13] Hardy, G.H., Wright, E.M.: An introduction to the theory of numbers, 4th ed. Oxford: Oxford University Press 1960 · Zbl 0086.25803 [14] Hurwitz, A.: Der Euklidische Divisionssatz in einem endlichen algebraischen Zahlkörper. Math. Z.3, 123-126 (1919) · JFM 47.0142.02 [15] Lakein, R.B.: Euclid’s algorithm in complex quartic fields. Acta Arith.20, 393-400 (1972) · Zbl 0224.12001 [16] Lang, S.: Algebraic number theory. Reading Mass.: Addison Wesley 1970 · Zbl 0211.38404 [17] Leech, J.: Some sphere packings in higher space. Canad. J. Math.16, 657-682 (1964) · Zbl 0142.20201 [18] Leech, J.: Notes on sphere packings. Canad. J. Math.19, 251-267 (1967) · Zbl 0162.25901 [19] Lekkerkerker, C.G.: Geometry of numbers. Groningen-Amsterdam: Wolters-Noordhoff-North Holland 1969 [20] Lenstra, Jr., H.W.: Euclid’s algorithm in cyclotomic fields. J. London Math. Soc.10, 457-465 (1975) · Zbl 0313.12001 [21] Lenstra, Jr., H.W.: Private communication [22] Markanda, R.: Euclidean rings of algebraic numbers and functions. J. Algebra37, 425-446 (1975) · Zbl 0321.12001 [23] Matzat, B.H.: Zahlentheoretische Programme und einige Ergebnisse. Universität Karlsruhe, 1969 [24] Nagell, T.: Sur une propriété des unités d’un corps algébrique. Ark. Mat.5, 343-356 (1964) · Zbl 0128.03403 [25] Nagell, T.: Quelques problèmes relatifs aux unités algébriques. Ark. Mat.8, 115-127 (1969) · Zbl 0213.06902 [26] Nagell, T.: Sur un type particulier d’unités algébriques. Ark. Mat.8, 163-184 (1969) · Zbl 0213.06901 [27] Ojala, T.: Euclid’s algorithm in the cyclotomic fieldQ(?16). To appear · Zbl 0349.12004 [28] O’Meara, O.T.: On the finite generation of linear groups over Hasse domains. J. Reine Angew. Math.217, 79-108 (1965) · Zbl 0128.25502 [29] Pohst, M.: Berechnung kleiner Diskriminanten total reeller algebraischer Zahlkörper. J. Reine Angew. Math.278/279, 278-300 (1975) · Zbl 0314.12014 [30] Poitou, G.: Minorations de discriminants (d’après A.M. Odlyzko). Sém. Bourbaki28, exp. 479 (1975/76) [31] Queen, C.S.: Euclidean subrings of global fields. Bull. Amer. Math. Soc.79, 437-439 (1973) · Zbl 0261.12001 [32] Rogers, C.A.: Packing and covering. Cambridge: Cambridge University Press 1964 · Zbl 0176.51401 [33] Smith, J.R.: On Euclid’s algorithm in some cyclic cubic fields. J. London Math. Soc.44, 577-582 (1969) · Zbl 0175.04501 [34] Smith, J.R.: The inhomogeneous minima of some totally real cubic fields, pp. 223-224. In: Computers in number theory, A.O.L., Atkin, B.J., Birch, eds. London: Academic Press 1971 · Zbl 0238.12004 [35] Taylor, E.M.: Euclid’s algorithm in cubic fields with complex conjugates. J. London Math. Soc.,14, 49-54 (1976) · Zbl 0358.12002 [36] Wasén, R.: On sequences of algebraic integers in pure extensions of prime degree. Colloq. Math.30, 89-104 (1974) 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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.