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Mathematics of Computation

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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?)

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  • 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. R. Greenberg, On the Iwasawa invariants of totally real number fields, Amer. J. Math. 98 (1976), 263--284. MR 53:5529
  • 4. H. Hasse, Über die Klassenzahl abelscher Zahlkörper, Akademie Verlag, Berlin, 1952. MR 14:141a
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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

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

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