On an algorithm of Billevich for finding units in algebraic fields
HTML articles powered by AMS MathViewer
- by Ray Steiner and Ronald Rudman PDF
- Math. Comp. 30 (1976), 598-609 Request permission
Abstract:
The well-known algorithm of Billevich for finding units in algebraic number fields is derived by algebraic methods. Some tables of units in cubic and quartic fields are given.References
-
W. E. H. BERWICK, "Algebraic number fields with two independent units," Proc. London Math. Soc., v. 34 (2), 1932, pp. 360-378.
- K. K. Billevič, On units of algebraic fields of third and fourth degree, Mat. Sb. N.S. 40(82) (1956), 123–136 (Russian). MR 0088516
- K. K. Billevič, Letter to the editor, Mat. Sb. (N.S.) 48 (49) (1959), 256 (Russian). MR 0123554
- K. K. Billevič, A theorem on unit elements of algebraic fields of order $n$, Mat. Sb. (N.S.) 64 (106) (1964), 145–152 (Russian). MR 0163902
- A. I. Borevich and I. R. Shafarevich, Number theory, Pure and Applied Mathematics, Vol. 20, Academic Press, New York-London, 1966. Translated from the Russian by Newcomb Greenleaf. MR 0195803
- B. N. Delone and D. K. Faddeev, Theory of Irrationalities of Third Degree, Acad. Sci. URSS. Trav. Inst. Math. Stekloff, 11 (1940), 340 (Russian). MR 0004269
- Ove Hemer, On the solvability of the Diophantine equation $ax^2+by^2+cz^2=0$ in imaginary Euclidean quadratic fields, Ark. Mat. 2 (1952), 57–82. MR 49917, DOI 10.1007/BF02591382
- Ove Hemer, Notes on the Diophantine equation $y^2-k=x^3$, Ark. Mat. 3 (1954), 67–77. MR 61115, DOI 10.1007/BF02589282
- Hymie London and Raphael Finkelstein, On Mordell’s equation $y^{2}-k=x^{3}$, Bowling Green State University, Bowling Green, Ohio, 1973. MR 0340172
- Henry B. Mann, Introduction to algebraic number theory, Ohio State University Press, Columbus, Ohio, 1955. With a chapter by Marshall Hall, Jr. MR 0072174 G. F. VORONOĬ, On a Generalization of the Algorithm of Continued Fractions, Doctoral Dissertation, Warsaw, 1896. (Russian) H. C. WILLIAMS & C. R. ZARNKE, A Table of Fundamental Units for Cubic Fields, Scientific Report No. 63, University of Manitoba, 1973.
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Math. Comp. 30 (1976), 598-609
- MSC: Primary 12A45
- DOI: https://doi.org/10.1090/S0025-5718-1976-0404204-8
- MathSciNet review: 0404204