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Voronoĭ-algorithm expansion of two families with period length going to infinity

Author: Brigitte Adam
Journal: Math. Comp. 64 (1995), 1687-1704
MSC: Primary 11R16; Secondary 11R27, 11Y40
MathSciNet review: 1308446
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Abstract: We consider families of orders of complex cubic fields introduced recently by Levesque and Rhin and find the Voronoï-algorithm expansions and the fundamental units. We compare with the Jacobi-Perron algorithm expansions.

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  • [1] B. N. Delone and D. K. Faddeev, The theory of irrationalities of the third degree, Translations of Mathematical Monographs, Vol. 10, American Mathematical Society, Providence, R.I., 1964. MR 0160744
  • [2] E. Dubois, Approximations diophantiennes simultanées de nombres algébriques. Calcul des meilleures approximations, Thèse de doctorat d'état, Univ. Pierre et Marie Curie, Paris, 1980.
  • [3] E. Dubois and A. Farhane, Unité fondamentale dans des familles d’ordres cubiques, Utilitas Math. 47 (1995), 97–115 (French, with French summary). MR 1330891
  • [4] A. Fahrane, Spécialisation de points extrémaux. Applications aux fractions continues et aux unités d'une famille de corps cubiques, Thèse, Univ. Caen, 1992.
  • [5] F. Halter-Koch, Einige periodische Kettenbruchentwicklungen und Grundeinheiten quadratischer Ordnungen, Abh. Math. Sem. Univ. Hamburg 59 (1989), 157–169 (German). MR 1049893, 10.1007/BF02942326
  • [6] J. Kühner, On a family of generalized continued fraction expansions with period length going to infinity, J. Number Theory (to appear).
  • [7] C. Levesque and G. Rhin, Two families of periodic Jacobi algorithms with period lengths going to infinity, J. Number Theory 37 (1991), no. 2, 173–180. MR 1092604, 10.1016/S0022-314X(05)80035-6
  • [8] Stéphane Louboutin, Minorations d’unités fondamentales—applications, Nagoya Math. J. 130 (1993), 1–18 (French). MR 1223726
  • [9] Oskar Perron, Grundlagen für eine Theorie des Jacobischen Kettenbruchalgorithmus, Math. Ann. 64 (1907), no. 1, 1–76 (German). MR 1511422, 10.1007/BF01449880
  • [10] Hans-Joachim Stender, Eine Formel für Grundeinheiten in reinen algebraischen Zahlkörpern dritten, vierten und sechsten Grades, J. Number Theory 7 (1975), 235–250 (German). MR 0369317
  • [11] G. F. Voronoi, On a generalization of the algorithm of continued fractions, Doctoral Dissertation, Warsaw, 1896 (in Russian).
  • [12] H. C. Williams, The period length of Voronoĭ’s algorithm for certain cubic orders, Publ. Math. Debrecen 37 (1990), no. 3-4, 245–265. MR 1082304

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Article copyright: © Copyright 1995 American Mathematical Society