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

 

Computation of $\Bbb Z_3$-invariants
of real quadratic fields


Author: Hisao Taya
Journal: Math. Comp. 65 (1996), 779-784
MSC (1991): Primary 11R23, 11R11, 11R27, 11Y40
MathSciNet review: 1333326
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Abstract: Let $k$ be a real quadratic field and $p$ an odd prime number which splits in $k$. In a previous work, the author gave a sufficient condition for the Iwasawa invariant $\lambda_p(k)$ of the cyclotomic $\Z_p$-extension of $k$ to be zero. The purpose of this paper is to study the case $p=3$ of this result and give new examples of $k$ with $\lambda_3(k)=0$, by using information on the initial layer of the cyclotomic $\Z_3$-extension of $k$.


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Additional Information

Hisao Taya
Affiliation: Department of Mathematics, School of Science and Engineering, Waseda University 3-4-1, Okubo Shinjuku-ku, Tokyo 169, Japan
Email: taya@cfi.waseda.ac.jp

DOI: http://dx.doi.org/10.1090/S0025-5718-96-00721-1
PII: S 0025-5718(96)00721-1
Keywords: Iwasawa invariants, real quadratic fields, unit groups, computation
Received by editor(s): October 12, 1993
Received by editor(s) in revised form: August 2, 1994
Article copyright: © Copyright 1996 American Mathematical Society