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

Author(s): Takashi Fukuda; Keiichi Komatsu.
Journal: Math. Comp. 70 (2001), 1707-1712.
MSC (2000): Primary 11R23, 11R27, 11Y40
Posted: November 13, 2000
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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.

References:

1.
H. Cohen, A course in computational algebraic number theory, Graduate Texts in Math., 138, Springer-Verlag, New York, Heidelberg, Berlin, 1993. MR 94i:11105
2.
T. Fukuda, A remark on the norm of cyclotomic units, (in Japanese) Sugaku 48 (1996), 89-90.
3.
T. Fukuda, K. Komatsu, M. Ozaki and H. Taya, On Iwasawa $\lambda_p$-invariants of relative real cyclic extensions of degree $p$, Tokyo J. Math. 20-2 (1997) 475-480. MR 98k:11153
4.
T. Fukuda and H. Taya, Computational research of Greenberg's conjecture for real quadratic fields, Mem. School Sci. Eng., Waseda Univ. 58 (1994), 175-203. MR 96b:11143
5.
R. Gold and J. Kim, Bases for cyclotomic units, Compositio Math. 71 (1989), 12-27. MR 90h:11101
6.
R. Greenberg, On the Iwasawa invariants of totally real number fields, Amer. J. Math. 98 (1976), 263-284. MR 53:5529
7.
H. Hasse, Über die Klassenzahl abelscher Zahlkörper, Akademie Verlag, Berlin, 1952. MR 14:141a
8.
A. Inatomi, On ${\mathbb{Z}}_p$-extensions of real abelian fields, Kodai Math. J. 12 (1989), 420-422. MR 90i:11119
9.
M. Ozaki and G. Yamamoto, Iwasawa $\lambda_3$-invariants of certain cubic fields, preprint
10.
W. Sinnott, On the Stickelberger ideal and the circular units of an abelian field, Inv. Math. 62 (1980), 181-234. MR 82i:12004
11.
H. Taya, On p-adic zeta functions and ${\mathbb{Z}}_p$-extensions of certain totally real number fields, Tohoku Math. J. 51 (1999), 21-33. MR 2000b:11121

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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: 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
Posted: November 13, 2000
Copyright of article: Copyright 2000, American Mathematical Society

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