Available in electronic format
Available in print format		 Mathematics of Computation
Journal of the American Mathematical Society
ISSN 1088-6842(e) ISSN 0025-5718(p)
Previous issue | Table of contents | Next issue
Articles in press | Recently posted articles | Most recent issue | All issues
Previous Article | Next Article
     

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
Retrieve article in: PDF
This article is available free of charge

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:

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

Similar Articles:

Retrieve articles in Mathematics of Computation with MSC (1991): 11R30, 11R22, 11Y40

Retrieve articles in all Journals with MSC (1991): 11R30, 11R22, 11Y40

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: 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
Copyright of article: Copyright 1996, American Mathematical Society

  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2009, American Mathematical Society
Privacy Statement 		Search the AMSPowered by Google