ArticleOriginal scientific text

Title

Généralisation d'une famille de Shanks

Authors 1

Affiliations

  1. Département de Mathématiques, URA CNRS 399, UFR MIM, Université de Metz, Ile du Saulcy, 57045 Metz Cedex 01, France

Bibliography

  1. B. Adam, Voronoï-algorithm expansion of two families with period length going to infinity, Math. Comp. 64 (1995), 1687-1704.
  2. L. Bernstein, The Jacobi-Perron Algorithm, its Theory and Application, Lecture Notes in Math. 207, Springer, Berlin, 1971.
  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.
  4. E. Dubois et A. Farhane, Unité fondamentale dans des familles d'ordres cubiques, Utilitas Math. 47 (1995), 97-115.
  5. A. Farhane, Spécialisation de points extrémaux. Application aux fractions continues et aux unités d'une famille de corps cubiques, thèse, Caen, 1992.
  6. F. Halter-Koch, Einige periodische Kettenbruchentwicklungen und Grundeinheiten quadratischer Ordnungen, Abh. Math. Sem. Univ. Hamburg 59 (1989), 157-169.
  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.
  8. R. A. Mollin and H. C. Williams, Consecutive powers in continued fractions, Acta Arith. 61 (1992), 233-264.
  9. O. Perron, Grundlagen für eine Theorie des Jacobischen Kettenbruchalgorithmus, Math. Ann. 64 (1907), 1-76.
  10. D. Shanks, On Gauss's class number problems, Math. Comp. 23 (1969), 151-163.
  11. G. F. Voronoï, On a generalization of the algorithm of continued fractions, Doctoral Dissertation, Warszawa, 1896 (en russe).
  12. H. C. Williams, Some generalizations of the Sn sequence of Shanks, Acta Arith. 69 (1995), 199-215.
Pages:
43-58
Main language of publication
French
Received
1997-04-21
Accepted
1997-08-19
Published
1998
Exact and natural sciences