References
Bergmann, G., Zur numerischen Bestimmung einer Einheitsbasis, Math. Annalen166, 103–105 (1966).
Bernstein, L., “Periodical Continued Fractions” of degree n by Jacobi's Algorithm, Jr. f.d. Reine Angew. Math.,213, 31–38 (1964).
Bernstein, L. New Infinite Classes of Periodic Jacobi-Perron Algorithms, Pacific Jr. Math.,16, 1–31 (1965
Bernstein, L. A 3-Dimensional Periodic Jacobi-Perron Algorithm of length 8, Jr. Number Theory, Vol.4, 48–69 (1972)
Bernstein, L. Representation of the n-th root of Dn-d as a Periodic Continued Fraction by Jacobi's Algorithm, Math. Nachrichten,1019, 179–200 (1965).
Bernstein, L. Periodicity of Jacobi's Algorithm for a special type of Cubic Irrationals, Jr. f.d. Reine Angew. Math.213, 134–146 (1964)
Bernstein, L. Periodische Jacobi-Perronsche Algorithmen, Archiv der Math.,15, 421–429 (1964).
Bernstein, L. Einheitenberechnung in Kubischen Keorpern mittels der Jacobi-Perronschen Algorithmus aus der Rechenanlage, Jr. f.d. Reine Angew. Math.,244, 201–220 (1970)
Bernstein, L. Infinite non-solubility Classes of the Delaunay-Nagell Equation, Jr. London Math. Soc., Vol.3, Part 1, 118–120 (1971)
Units and Diophantine Equations in Algebraic Number Fields of degree n=2,3,..., Symposia Mathematica 9 Istituto Nazionale di Alta Matematica, in print.
—— and Hasse H., Einheitenberechnung mittels des Jacobi-Perronschen Algorithmus, Jr. f.d. Reine Angew. Math.,218, 51–69 (1965).
Bilevich, K. K., On the Units of Algebraic Number Fields of the Third and Fourth Degree, Math. Sbornik,40, 123–136 (Russian) (1956).
Finkelstein, R., On the Units in a Quadratic Field with Applications to Mordell Equation, Doctoral Dissertation, Arizona State Univ., (1968).
and London, H., On Mordells Equation y2−k=x3, Bowling Green State Univ. Press, 1–146 (1973).
Jacobi, C. G. J., Allgemeine Theorie der kettenbruchaehnlichen Algorithmen etc., Jr. f.d. Reine Angew. Math., 69, 29–64 (1869).
Nagell, M. T., Solution Complete de quelques equations cubiques a deux indetermines, Jr. Math. Pures Appl., 209–270 (1925).
Perron O., Grundlagen fuer eine Theorie des Jacobischen Kettenbruch algorithmus, Math. Annalen,64, 1–76 (1907).
Stender, H. J., Ueber die Grundeinheit fuer spezielle unendliche Klassen reiner kubischer Zahlkoerper, Abh. Math. Semonar Univ. Hamburg,33, 203–215 (1969). Grundeinheiten fuer einige unendliche Klassen reiner biquadratischer Zahlkoerper etc., Jr. f.d. Reine Angew. Math., in print.
Szekerres, G., Multidimensional Continued Fractions, Annales Univ. Sc. Budapestinensis De Rolando Eotvos Nom., Sectio Math., Vol. XIII, 113–140 (1970).
Zassenhaus, H., On the Units of Orders, Jr. of Algebra, Vol.20, 368–396 (1972).
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Bernstein, L. Units from periodic Jacobi-Perron algorithms in algebraic number fields of degree n>2. Manuscripta Math 14, 249–261 (1974). https://doi.org/10.1007/BF01171411
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DOI: https://doi.org/10.1007/BF01171411