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Transactions of the American Mathematical Society

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The generalized Pellian equation


Author: Leon Bernstein
Journal: Trans. Amer. Math. Soc. 127 (1967), 76-89
MSC: Primary 10.11
MathSciNet review: 0207635
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  • 1. Leon Bernstein, Periodical continued fractions for irrationals of degree 𝑛 by Jacobi’s algorithm, J. Reine Angew. Math. 213 (1963/1964), 31–38. MR 0155793
  • 2. -1(b). Representation of $ {({D^n} - d)^{1/n}}$ as a periodic continued fraction by Jacobi's algorithm, Math. Nachr. 1019 (1965), 179-200.
  • 3. -1(c). Periodicity of Jacobi's algorithm for a special type of cubic irrationals, J. Reine Angew. Math. 213 (1964), 134-146.
  • 4. Leon Bernstein, Periodische Jacobische Algorithmen für eine unendliche Klasse algebraischer Irrationalzahlen vom Grade 𝑁 und einige unendliche Klassen kubischer Irrationalzahlen, J. Reine Angew. Math. 214/215 (1964), 76–83. MR 0160756
  • 5. Leon Bernstein, Periodische Jacobi-Perronsche Algorithmen, Arch. Math. (Basel) 15 (1964), 421–429 (German). MR 0169816
  • 6. Leon Bernstein, New infinite classes of periodic Jacobi-Perron algorithms, Pacific J. Math. 16 (1966), 439–469. MR 0190091
  • 7. Leon Bernstein, A periodic Jacobi-Perron algorithm, Canad. J. Math. 17 (1965), 933–945. MR 0181611
  • 8. Leon Bernstein and Helmut Hasse, Einheitenberechnung mittels des Jacobi-Perronschen Algorithmus, J. Reine Angew. Math. 218 (1965), 51–69 (German). MR 0180530
  • 9. Leon Bernstein, Rational approximations of algebraic irrationals by means of a modified Jacobi-Peron algorithm, Duke Math. J. 32 (1965), 161–176. MR 0175847
  • 10. Leon Bernstein, Periodische Kettenbrüche beliebiger Periodenlänge, Math. Z. 86 (1964), 128–135 (German). MR 0168525
  • 11. -1(k). Rational approximation of algebraic numbers, Proc. Nat. Conf. on Data Processing, pp. 91-105, Rehovoth, Israel Proc. Assoc., 1964.
  • 12. -1(l). Explicit solution of an algebraic equation of degree n by means of a modified Jacobi-Perron algorithm, SIAM Rev. (to appear).
  • 13. Leon Bernstein, The modified algorithm of Jacobi-Perron, Mem. Amer. Math. Soc. No. 67 (1966), 44. MR 0205446
  • 14. Leon Bernstein, Der 𝐵-Algorithmus und siene Anwendung, J. Reine Angew. Math. 227 (1967), 150–177 (German). MR 0215782
  • 15. -1(p). Ein neuer Algorithmus Auer alsteigende Basispotenzen im Kubischen Koerper, Math. Nachr. Naas Feitschrift, 1967.
  • 16. -1(q). Periodic algorithms and units of algebraic fields, Hamburger Einzelhefte (to appear).
  • [C] G. J. Jacobi 2. Allgemeine Theorie der Kettenbruchähnlichen Algorithm, in welchen jede Zahl aus drei vorherfehenden gebildet wird, J. Reine Angew. Math. 69 (1868).
  • 17. Oskar Perron, Grundlagen für eine Theorie des Jacobischen Kettenbruchalgorithmus, Math. Ann. 64 (1907), no. 1, 1–76 (German). MR 1511422, 10.1007/BF01449880

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DOI: https://doi.org/10.1090/S0002-9947-1967-0207635-5
Article copyright: © Copyright 1967 American Mathematical Society