Mathematics of Computation

Author(s): Takashi Fukuda.
Journal: Math. Comp. 65 (1996), 1339-1348.
MSC (1991): Primary 11R23, 11R11, 11R27, 11Y40
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Abstract: We give new examples of real quadratic fields $k$

for which the Iwasawa invariant $\lambda _3(k)$ and $\mu _3(k)$ are both zero by calculating cyclotomic units of real cyclic number fields of degree 18.

1.: T. Fukuda, Iwasawa's $\lambda$ -invariants of certain real quadratic fields, Proc. Japan Acad. 65, (1989), 260--262. MR 91b:11115
2.: T. Fukuda and H. Taya, The Iwasawa $\lambda$ -invariants of $\mathbb {Z} _p$ -extensions of real quadratic fields, Acta Arith. 69 (1995), 277--292.
3.: R. Greenberg, On the Iwasawa invariants of totally real number fields, Amer. J. Math. 98 (1976), 263--284. MR 53:5529
4.: H. Hasse, Über die Klassenzahl abelscher Zahlkörper, Akademie Verlag, Berlin, 1952. MR 14:141a
5.: S. Mäki, The determination of units in real cyclic sextic fields, Lecture Notes in Math., vol. 797, Springer--Verlag, Berlin, Heidelberg, New York, 1980. MR 82a:12004
6.: H. Taya, Computation of $\mathbb {Z} _3$ -invariants of real quadratic fields, Math. Comp. 65 (1996), 779--784. CMP 95:13

Retrieve articles in Mathematics of Computation with MSC (1991): 11R23, 11R11, 11R27, 11Y40

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

DOI: 10.1090/S0025-5718-96-00730-2
PII: S 0025-5718(96)00730-2
Keywords: Iwasawa invariants, real quadratic fields, unit groups, computation
Received by editor(s): January 10, 1995
Dedicated: Dedicated to Professor Hisashi Ogawa on his 70th birthday
Copyright of article: Copyright 1996, American Mathematical Society

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