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Brunotte, Horst; Huszti, Andrea; Pethő, Attila
Bases of canonical number systems in quartic algebraic number fields. Journal de théorie des nombres de Bordeaux, 18 no. 3 (2006), p. 537-557
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Résumé

Les systčmes canoniques de numération peuvent ętre considérés comme des généralisations naturelles de la numération classique des entiers. Dans la présente note, une modification d’un algorithme de B. Kovács et A. Pethő est établie et appliquée au calcul des systčmes canoniques de numération dans certains anneaux d’entiers de corps de nombres algébriques. L’algorithme permet de déterminer tous les systčmes canoniques de numération de quelques corps de nombres de degré quatre.

Bibliographie

[1] S. Akiyama, T. Borbély, H. Brunotte, A. Pethő and J. M. Thuswaldner, On a generalization of the radix representation – a survey, in “High Primes and Misdemeanours: lectures in honour of the 60th birthday of Hugh Cowie Williams”, Fields Institute Commucations, vol. 41 (2004), 1927.  Zbl 02154268
[2] S. Akiyama, T. Borbély, H. Brunotte, A. Pethő and J. M. Thuswaldner, Generalized radix representations and dynamical systems I, Acta Math. Hung., 108 (2005), 207238.  MR 2162561 |  Zbl 02213307
[3] S. Akiyama, H. Brunotte and A. Pethő, Cubic CNS polynomials, notes on a conjecture of W.J. Gilbert, J. Math. Anal. and Appl., 281 (2003), 402415.  MR 1980100 |  Zbl 1021.11005
[4] S. Akiyama and H. Rao, New criteria for canonical number systems, Acta Arith., 111 (2004), 525.  MR 2038059 |  Zbl 1049.11008
[5] S. Akiyama and J. M. Thuswaldner, On the topological structure of fractal tilings generated by quadratic number systems, Comput. Math. Appl. 49 (2005), no. 9-10, 14391485.  MR 2149493 |  Zbl 02201728
[6] T. Borbély, Általánosított számrendszerek, Master Thesis, University of Debrecen, 2003.
[7] H. Brunotte, On trinomial bases of radix representations of algebraic integers, Acta Sci. Math. (Szeged), 67 (2001), 521527.  MR 1876451 |  Zbl 0996.11067
[8] H. Brunotte, On cubic CNS polynomials with three real roots, Acta Sci. Math. (Szeged), 70 (2004), 495 – 504.  MR 2107523 |  Zbl 1064.11005
[9] I. Gaál, Diophantine equations and power integral bases, Birkhäuser (Berlin), (2002).  MR 1896601 |  Zbl 1016.11059
[10] W. J. Gilbert, Radix representations of quadratic fields, J. Math. Anal. Appl., 83 (1981), 264274.  MR 632342 |  Zbl 0472.10011
[11] E. H. Grossman, Number bases in quadratic fields, Studia Sci. Math. Hungar., 20 (1985), 5558.  MR 886005 |  Zbl 0562.12004
[12] V. Grünwald, Intorno all’aritmetica dei sistemi numerici a base negativa con particolare riguardo al sistema numerico a base negativo-decimale per lo studio delle sue analogie coll’aritmetica ordinaria (decimale), Giornale di matematiche di Battaglini, 23 (1885), 203221, 367.  JFM 17.0120.02
[13] K. Győry, Sur les polynômes ŕ coefficients entiers et de discriminant donné III, Publ. Math. (Debrecen), 23 (1976), 141165.  MR 437491 |  Zbl 0354.10041
[14] I. Kátai and B. Kovács, Kanonische Zahlensysteme in der Theorie der quadratischen algebraischen Zahlen, Acta Sci. Math. (Szeged), 42 (1980), 99107.  MR 576942 |  Zbl 0386.10007
[15] I. Kátai and B. Kovács, Canonical number systems in imaginary quadratic fields, Acta Math. Acad. Sci. Hungar., 37 (1981), 159164.  MR 616887 |  Zbl 0477.10012
[16] I. Kátai and J. Szabó, Canonical number systems for complex integers, Acta Sci. Math. (Szeged), 37 (1975), 255260.  MR 389759 |  Zbl 0309.12001
[17] D. E. Knuth, An imaginary number system, Comm. ACM, 3 (1960), 245 – 247.  MR 127508
[18] D. E. Knuth, The Art of Computer Programming, Vol. 2 Semi-numerical Algorithms, Addison Wesley (1998), London 3rd edition.  MR 633878 |  Zbl 0895.65001
[19] B. Kovács, Canonical number systems in algebraic number fields, Acta Math. Acad. Sci. Hungar., 37 (1981), 405407.  MR 619892 |  Zbl 0505.12001
[20] B. Kovács and A. Pethő, Number systems in integral domains, especially in orders of algebraic number fields, Acta Sci. Math. (Szeged), 55 (1991), 287299.  MR 1152592 |  Zbl 0760.11002
[21] S. Körmendi, Canonical number systems in ${{\mathbb{Q}}(\@root 3 \of {2})}$, Acta Sci. Math. (Szeged), 50 (1986), 351357.  MR 882046 |  Zbl 0616.10007
[22] G. Lettl and A. Pethő, Complete solution of a family of quartic Thue equations, Abh. Math. Sem. Univ. Hamburg 65 (1995), 365383.  MR 1359142 |  Zbl 0853.11021
[23] M. Mignotte, A. Pethő and R. Roth, Complete solutions of quartic Thue and index form equations, Math. Comp. 65 (1996), 341354.  MR 1316596 |  Zbl 0853.11022
[24] P. Olajos, Power integral bases in the family of simplest quartic fields, Experiment. Math. 14 (2005), 129132.
Article |  MR 2169516 |  Zbl 1092.11042
[25] A. Pethő, On a polynomial transformation and its application to the construction of a public key cryptosystem, Computational Number Theory, Proc., Walter de Gruyter Publ. Comp. Eds.: A. Pethő, M. Pohst, H. G. Zimmer and H. C. Williams (1991), 3143.  MR 1151853 |  Zbl 0733.94014
[26] A. Pethő, Notes on CNS polynomials and integral interpolation, More sets, graphs and numbers, 301315, Bolyai Soc. Math. Stud., 15, Springer, Berlin, 2006.  MR 2223397 |  Zbl 05037084
[27] A. Pethő, Connections between power integral bases and radix representations in algebraic number fields, Proc. of the 2003 Nagoya Conf. “Yokoi-Chowla Conjecture and Related Problems”, Furukawa Total Pr. Co. (2004), 115125.
[28] R. Robertson, Power bases for cyclotomic integer rings, J. Number Theory, 69 (1998), 98118.  MR 1611089 |  Zbl 0923.11150
[29] R. Robertson, Power bases for 2-power cyclotomic integer rings, J. Number Theory, 88 (2001), 196209.  MR 1825999 |  Zbl 0973.11091
[30] K. Scheicher, Kanonische Ziffernsysteme und Automaten, Grazer Math. Ber., 333 (1997), 117.  MR 1640469 |  Zbl 0905.11009
[31] D. Shanks, The simplest cubic fields, Math. Comp., 28 (1974), 11371152.  MR 352049 |  Zbl 0307.12005
[32] J. M. Thuswaldner, Elementary properties of canonical number systems in quadratic fields, in: Applications of Fibonacci Numbers, Volume 7, G. E. Bergum et al. (eds.), Kluwer Academic Publishers, Dordrecht (1998), 405414.  MR 1638467 |  Zbl 0917.11054
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