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

Author(s): T. Fukuda; K. Komatsu.
Journal: Math. Comp. 65 (1996), 313-318.
MSC (1991): Primary 11R30, 11R22, 11Y40
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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:

1: R. Greenberg, On the Iwasawa invariants of totally real number fields, Amer. J. Math. 98 (1976), 263--284.MR 53:5529
2: H. Hasse, Über die Klassenzahl abelscher Zahlkörper, Akademie Verlag, Berlin, 1952.MR 14:141
3: S. Mäki, The determination of units in real cyclic sextic fields, Lecture Notes in Math., vol. 797, Springer--Verlag, Berlin, Heidelberg, New York, 1980.MR 82a:12004


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