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

 

A Capitulation Problem and Greenberg's
Conjecture on Real Quadratic Fields


Authors: T. Fukuda and K. Komatsu
Journal: Math. Comp. 65 (1996), 313-318
MSC (1991): Primary 11R30, 11R22, 11Y40
MathSciNet review: 1322890
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Abstract | References | Similar Articles | Additional Information

Abstract: We give a sufficient condition in order that an ideal of a real quadratic field $F$ capitulates in the cyclotomic $\Z_3$-extension of $F$ by using a unit of an intermediate field. Moreover, we give new examples of $F$'s for which Greenberg's conjecture holds by calculating units of fields of degree 6, 18, 54 and 162.


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Additional Information

T. 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

K. Komatsu
Affiliation: Department of Mathematics, Tokyo University of Agriculture and Technology, Fuchu, Tokyo, Japan

DOI: http://dx.doi.org/10.1090/S0025-5718-96-00676-X
PII: S 0025-5718(96)00676-X
Keywords: Iwasawa invariants, real quadratic fields, unit groups, computation
Received by editor(s): September 26, 1994
Received by editor(s) in revised form: February 11, 1995
Article copyright: © Copyright 1996 American Mathematical Society