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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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On the Iwasawa $\lambda$-invariant of the cyclotomic $\mathbb {Z}_2$-extension of $\mathbb {Q}(\sqrt {p} )$
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by Takashi Fukuda and Keiichi Komatsu PDF
Math. Comp. 78 (2009), 1797-1808 Request permission

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
  • 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
  • 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
  • © Copyright 2009 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 78 (2009), 1797-1808
  • MSC (2000): Primary 11G15, 11R27, 11Y40
  • DOI: https://doi.org/10.1090/S0025-5718-09-02124-3
  • MathSciNet review: 2501076