Généralisation d'une famille de Shanks

Brigitte Adam

Acta Arithmetica (1998)

  • Volume: 84, Issue: 1, page 43-58
  • ISSN: 0065-1036

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Brigitte Adam. "Généralisation d'une famille de Shanks." Acta Arithmetica 84.1 (1998): 43-58. <http://eudml.org/doc/207134>.

@article{BrigitteAdam1998,
author = {Brigitte Adam},
journal = {Acta Arithmetica},
keywords = {family of quadratic fields of Shanks; fundamental units; continued fractions; Jacobi-Perron algorithm; Voronoi algorithm; Voronoï algorithm},
language = {fre},
number = {1},
pages = {43-58},
title = {Généralisation d'une famille de Shanks},
url = {http://eudml.org/doc/207134},
volume = {84},
year = {1998},
}

TY - JOUR
AU - Brigitte Adam
TI - Généralisation d'une famille de Shanks
JO - Acta Arithmetica
PY - 1998
VL - 84
IS - 1
SP - 43
EP - 58
LA - fre
KW - family of quadratic fields of Shanks; fundamental units; continued fractions; Jacobi-Perron algorithm; Voronoi algorithm; Voronoï algorithm
UR - http://eudml.org/doc/207134
ER -

References

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  1. [1] B. Adam, Voronoï-algorithm expansion of two families with period length going to infinity, Math. Comp. 64 (1995), 1687-1704. Zbl0858.11070
  2. [2] L. Bernstein, The Jacobi-Perron Algorithm, its Theory and Application, Lecture Notes in Math. 207, Springer, Berlin, 1971. Zbl0213.05201
  3. [3] B. N. Delone and D. K. Faddeev, The Theory of Irrationalities of the Third Degree, Transl. Math. Monographs 10, Amer. Math. Soc., Providence, R.I., 1964. Zbl0133.30202
  4. [4] E. Dubois et A. Farhane, Unité fondamentale dans des familles d'ordres cubiques, Utilitas Math. 47 (1995), 97-115. 
  5. [5] A. Farhane, Spécialisation de points extrémaux. Application aux fractions continues et aux unités d'une famille de corps cubiques, thèse, Caen, 1992. 
  6. [6] F. Halter-Koch, Einige periodische Kettenbruchentwicklungen und Grundeinheiten quadratischer Ordnungen, Abh. Math. Sem. Univ. Hamburg 59 (1989), 157-169. 
  7. [7] C. Levesque and G. Rhin, Two families of periodic Jacobi algorithms with period lengths going to infinity, J. Number Theory 37 (1991), 173-180. Zbl0723.11032
  8. [8] R. A. Mollin and H. C. Williams, Consecutive powers in continued fractions, Acta Arith. 61 (1992), 233-264. Zbl0764.11010
  9. [9] O. Perron, Grundlagen für eine Theorie des Jacobischen Kettenbruchalgorithmus, Math. Ann. 64 (1907), 1-76. Zbl38.0262.01
  10. [10] D. Shanks, On Gauss's class number problems, Math. Comp. 23 (1969), 151-163. Zbl0177.07103
  11. [11] G. F. Voronoï, On a generalization of the algorithm of continued fractions, Doctoral Dissertation, Warszawa, 1896 (en russe). 
  12. [12] H. C. Williams, Some generalizations of the S n sequence of Shanks, Acta Arith. 69 (1995), 199-215. Zbl0842.11004

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