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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

On Iwasawa $\lambda_3$-invariants of cyclic cubic fields of prime conductor


Authors: Takashi Fukuda and Keiichi Komatsu
Journal: Math. Comp. 70 (2001), 1707-1712
MSC (2000): Primary 11R23, 11R27, 11Y40
Published electronically: November 13, 2000
MathSciNet review: 1836928
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Abstract:

For certain cyclic cubic fields $k$, we verified that Iwasawa invariants $\lambda_3(k)$ vanished by calculating units of abelian number field of degree 27. Our method is based on the explicit representation of a system of cyclotomic units of those fields.


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Additional Information

Takashi Fukuda
Affiliation: Department of Mathematics, College of Industrial Technology, Nihon University, 2-11-1 Shin-ei, Narashino, Chiba, Japan
Email: fukuda@math.cit.nihon-u.ac.jp

Keiichi Komatsu
Affiliation: Department of Information and Computer Science, School of Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku, Tokyo 169, Japan
Email: kkomatsu@mse.waseda.ac.jp

DOI: http://dx.doi.org/10.1090/S0025-5718-00-01284-9
PII: S 0025-5718(00)01284-9
Keywords: Iwasawa invariant, cyclotomic unit, cubic field
Received by editor(s): August 5, 1999
Received by editor(s) in revised form: January 6, 2000
Published electronically: November 13, 2000
Article copyright: © Copyright 2000 American Mathematical Society