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Mathematics of Computation

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

Authors: Takashi Fukuda and Keiichi Komatsu
Journal: Math. Comp. 78 (2009), 1797-1808
MSC (2000): Primary 11G15, 11R27, 11Y40
Published electronically: January 28, 2009
MathSciNet review: 2501076
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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 $ p$ 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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Additional Information

Takashi Fukuda
Affiliation: Department of Mathematics, College of Industrial Technology, Nihon University, 2-11-1 Shin-ei, Narashino, Chiba, Japan

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

Keywords: Iwasawa invariants, real quadratic fields
Received by editor(s): May 30, 2007
Received by editor(s) in revised form: November 16, 2007
Published electronically: January 28, 2009
Dedicated: In memory of Professor H. Ogawa
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.