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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Cyclotomic Units and Greenberg's Conjecture
for Real Quadratic Fields


Author: Takashi Fukuda
Journal: Math. Comp. 65 (1996), 1339-1348
MSC (1991): Primary 11R23, 11R11, 11R27, 11Y40
MathSciNet review: 1344612
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Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • 1. Takashi Fukuda, Iwasawa’s 𝜆-invariants of certain real quadratic fields, Proc. Japan Acad. Ser. A Math. Sci. 65 (1989), no. 7, 260–262. MR 1030195 (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. Ralph Greenberg, On the Iwasawa invariants of totally real number fields, Amer. J. Math. 98 (1976), no. 1, 263–284. MR 0401702 (53 #5529)
  • 4. Helmut Hasse, Über die Klassenzahl abelscher Zahlkörper, Akademie-Verlag, Berlin, 1952 (German). MR 0049239 (14,141a)
  • 5. Sirpa Mäki, The determination of units in real cyclic sextic fields, Lecture Notes in Mathematics, vol. 797, Springer, Berlin, 1980. MR 584794 (82a:12004)
  • 6. H. Taya, Computation of $\mathbb {Z} _3$-invariants of real quadratic fields, Math. Comp. 65 (1996), 779--784. CMP 95:13

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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

DOI: http://dx.doi.org/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
Article copyright: © Copyright 1996 American Mathematical Society