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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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The generalized Pellian equation
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by Leon Bernstein PDF
Trans. Amer. Math. Soc. 127 (1967), 76-89 Request permission
References
  • Leon Bernstein, Periodical continued fractions for irrationals of degree $n$ by Jacobi’s algorithm, J. Reine Angew. Math. 213 (1963/64), 31–38. MR 155793, DOI 10.1515/crll.1964.213.31
    • —1(b). Representation of ${({D^n} - d)^{1/n}}$ as a periodic continued fraction by Jacobi’s algorithm, Math. Nachr. 1019 (1965), 179-200. —1(c). Periodicity of Jacobi’s algorithm for a special type of cubic irrationals, J. Reine Angew. Math. 213 (1964), 134-146.
  • 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 160756, DOI 10.1515/crll.1964.214-215.76
  • Leon Bernstein, Periodische Jacobi-Perronsche Algorithmen, Arch. Math. (Basel) 15 (1964), 421–429 (German). MR 169816, DOI 10.1007/BF01589226
  • Leon Bernstein, New infinite classes of periodic Jacobi-Perron algorithms, Pacific J. Math. 16 (1966), 439–469. MR 190091
  • Leon Bernstein, A periodic Jacobi-Perron algorithm, Canadian J. Math. 17 (1965), 933–945. MR 181611, DOI 10.4153/CJM-1965-089-9
  • Leon Bernstein and Helmut Hasse, Einheitenberechnung mittels des Jacobi-Perronschen Algorithmus, J. Reine Angew. Math. 218 (1965), 51–69 (German). MR 180530
  • Leon Bernstein, Rational approximations of algebraic irrationals by means of a modified Jacobi-Peron algorithm, Duke Math. J. 32 (1965), 161–176. MR 175847
  • Leon Bernstein, Periodische Kettenbrüche beliebiger Periodenlänge, Math. Z. 86 (1964), 128–135 (German). MR 168525, DOI 10.1007/BF01111333
    • —1(k). Rational approximation of algebraic numbers, Proc. Nat. Conf. on Data Processing, pp. 91-105, Rehovoth, Israel Proc. Assoc., 1964. —1(l). Explicit solution of an algebraic equation of degree n by means of a modified Jacobi-Perron algorithm, SIAM Rev. (to appear).
  • Leon Bernstein, The modified algorithm of Jacobi-Perron, Mem. Amer. Math. Soc. 67 (1966), 44. MR 205446
  • Leon Bernstein, Der $B$-Algorithmus und siene Anwendung, J. Reine Angew. Math. 227 (1967), 150–177 (German). MR 215782, DOI 10.1515/crll.1967.227.150
    • —1(p). Ein neuer Algorithmus Auer alsteigende Basispotenzen im Kubischen Koerper, Math. Nachr. Naas Feitschrift, 1967. —1(q). Periodic algorithms and units of algebraic fields, Hamburger Einzelhefte (to appear). G. J. Jacobi 2. Allgemeine Theorie der Kettenbruchähnlichen Algorithm, in welchen jede Zahl aus drei vorherfehenden gebildet wird, J. Reine Angew. Math. 69 (1868).
  • Oskar Perron, Grundlagen für eine Theorie des Jacobischen Kettenbruchalgorithmus, Math. Ann. 64 (1907), no. 1, 1–76 (German). MR 1511422, DOI 10.1007/BF01449880
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Additional Information
  • © Copyright 1967 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 127 (1967), 76-89
  • MSC: Primary 10.11
  • DOI: https://doi.org/10.1090/S0002-9947-1967-0207635-5
  • MathSciNet review: 0207635