A capitulation problem and Greenberg’s conjecture on real quadratic fields
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- by T. Fukuda and K. Komatsu PDF
- Math. Comp. 65 (1996), 313-318 Request permission
Abstract:
We give a sufficient condition in order that an ideal of a real quadratic field $F$ capitulates in the cyclotomic $\mathbb {Z}_3$-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
- Ralph Greenberg, On the Iwasawa invariants of totally real number fields, Amer. J. Math. 98 (1976), no. 1, 263–284. MR 401702, DOI 10.2307/2373625
- P. Hebroni, Sur les inverses des éléments dérivables dans un anneau abstrait, C. R. Acad. Sci. Paris 209 (1939), 285–287 (French). MR 14
- Sirpa Mäki, The determination of units in real cyclic sextic fields, Lecture Notes in Mathematics, vol. 797, Springer, Berlin, 1980. MR 584794, DOI 10.1007/BFb0088938
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
- Received by editor(s): September 26, 1994
- Received by editor(s) in revised form: February 11, 1995
- © Copyright 1996 American Mathematical Society
- Journal: Math. Comp. 65 (1996), 313-318
- MSC (1991): Primary 11R30, 11R22, 11Y40
- DOI: https://doi.org/10.1090/S0025-5718-96-00676-X
- MathSciNet review: 1322890