Mathematics of Computation

Author(s): Hisao Taya.
Journal: Math. Comp. 65 (1996), 779-784.
MSC (1991): Primary 11R23, 11R11, 11R27, 11Y40
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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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Retrieve articles in Mathematics of Computation with MSC (1991): 11R23, 11R11, 11R27, 11Y40

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: 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
Copyright of article: Copyright 1996, American Mathematical Society

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