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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.78.

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Cyclotomic units and Greenberg’s conjecture for real quadratic fields
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by Takashi Fukuda PDF
Math. Comp. 65 (1996), 1339-1348 Request permission

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.
References
  • Takashi Fukuda, Iwasawa’s $\lambda$-invariants of certain real quadratic fields, Proc. Japan Acad. Ser. A Math. Sci. 65 (1989), no. 7, 260–262. MR 1030195
  • T. Fukuda and H. Taya, The Iwasawa $\lambda$-invariants of $\mathbb {Z}_p$-extensions of real quadratic fields, Acta Arith. 69 (1995), 277–292.
  • Ralph Greenberg, On the Iwasawa invariants of totally real number fields, Amer. J. Math. 98 (1976), no. 1, 263–284. MR 401702, DOI 10.2307/2373625
  • P. Hebroni, Sur les inverses des éléments dérivables dans un anneau abstrait, C. R. Acad. Sci. Paris 209 (1939), 285–287 (French). MR 14
  • Sirpa Mäki, The determination of units in real cyclic sextic fields, Lecture Notes in Mathematics, vol. 797, Springer, Berlin, 1980. MR 584794, DOI 10.1007/BFb0088938
  • H. Taya, Computation of $\mathbb {Z}_3$-invariants of real quadratic fields, Math. Comp. 65 (1996), 779–784.
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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
  • Received by editor(s): January 10, 1995

  • Dedicated: Dedicated to Professor Hisashi Ogawa on his 70th birthday
  • © Copyright 1996 American Mathematical Society
  • Journal: Math. Comp. 65 (1996), 1339-1348
  • MSC (1991): Primary 11R23, 11R11, 11R27, 11Y40
  • DOI: https://doi.org/10.1090/S0025-5718-96-00730-2
  • MathSciNet review: 1344612