Mathematics of Computation

On the Iwasawa $\lambda$ -invariant of the cyclotomic $\mathbb{Z}_2$ -extension of $\mathbb{Q}(\sqrt{p} )$

Author(s): Takashi Fukuda; Keiichi Komatsu.
Journal: Math. Comp. 78 (2009), 1797-1808.
MSC (2000): Primary 11G15, 11R27, 11Y40
Posted: January 28, 2009
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Abstract: We study the Iwasawa $\lambda$ -invariant of the cyclotomic $\mathbb{Z}_2$ -extension of $\mathbb{Q}(\sqrt{p} )$ for an odd prime number

which satisfies $p\equiv 1\pmod{16}$ relating it to units having certain properties. We give an upper bound of $\lambda$ and show $\lambda=0$ in certain cases. We also give new numerical examples of $\lambda=0$ .

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Retrieve articles in Mathematics of Computation with MSC (2000): 11G15, 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

Keiichi Komatsu
Affiliation: Department of Mathematical Science, School of Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku, Tokyo 169-8555, Japan
Email: kkomatsu@waseda.jp

DOI: 10.1090/S0025-5718-09-02124-3
PII: S 0025-5718(09)02124-3
Keywords: Iwasawa invariants, real quadratic fields
Received by editor(s): May 30, 2007 and, in revised form November 16, 2007
Posted: January 28, 2009
Dedicated: In memory of Professor H. Ogawa
Copyright of article: Copyright 2009, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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