Généralisation d'une famille de Shanks

• Autorzy: Brigitte Adam
• Języki publikacji: FR

Kategorie tematyczne

• 11A55: Continued fractions
• 11R29: Class numbers, class groups, discriminants
• 11R27: Units and factorization
• 11Y65: Continued fraction calculations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1998
• Tom: 84
• Numer: 1
• Strony: 43-58

Daty

wydano

1998

otrzymano

1997-04-21

poprawiono

1997-08-19

Twórcy

autor

Brigitte Adam

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

Bibliografia

• [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 $S_n$ sequence of Shanks, Acta Arith. 69 (1995), 199-215.