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Mathematics of Computation

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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.

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

  • 1 Ralph Greenberg, On the Iwasawa invariants of totally real number fields, Amer. J. Math. 98 (1976), no. 1, 263–284. MR 0401702
  • 2 Helmut Hasse, Über die Klassenzahl abelscher Zahlkörper, Akademie-Verlag, Berlin, 1952 (German). MR 0049239
  • 3 Sirpa Mäki, The determination of units in real cyclic sextic fields, Lecture Notes in Mathematics, vol. 797, Springer, Berlin, 1980. MR 584794

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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

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

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