On the Euclidean nature of four cyclic cubic fields
Authors:
H. J. Godwin and J. R. Smith
Journal:
Math. Comp. 60 (1993), 421-423
MSC:
Primary 11R16; Secondary 11R04, 11R29, 11Y40
DOI:
https://doi.org/10.1090/S0025-5718-1993-1149291-7
MathSciNet review:
1149291
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: It is shown that the cyclic cubic fields with discriminants , and
are Euclidean
- [1] E. S. Barnes and H. P. F. Swinnerton-Dyer, The inhomogeneous minima of binary quadratic forms, Acta Math. 87 (1952), 259-322. MR 0053162 (14:730a)
- [2] H. Heilbronn, On Euclid's algorithm in cubic self-conjugate fields, Proc. Cambridge Philos. Soc. 46 (1950), 377-382. MR 0035313 (11:716a)
- [3] P. A. Samet, The product of non-homogeneous linear forms. I, Proc. Cambridge Philos. Soc. 50 (1954), 372-379. MR 0064820 (16:340d)
- [4] -, The product of non-homogeneous linear forms. II, Proc. Cambridge Philos. Soc. 50 (1954), 380-390. MR 0064821 (16:340e)
- [5] J. R. Smith, On Euclid's algorithm in some cyclic cubic fields, J. London Math. Soc. 44 (1969), 577-582. MR 0240075 (39:1429)
Retrieve articles in Mathematics of Computation with MSC: 11R16, 11R04, 11R29, 11Y40
Retrieve articles in all journals with MSC: 11R16, 11R04, 11R29, 11Y40
Additional Information
DOI:
https://doi.org/10.1090/S0025-5718-1993-1149291-7
Article copyright:
© Copyright 1993
American Mathematical Society