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The nonquadratic imaginary cyclic fields of  -power degrees with class numbers equal to their genus class numbers
Author(s):
Stéphane
Louboutin
Journal:
Proc. Amer. Math. Soc.
127
(1999),
355-361.
MSC (1991):
Primary 11R20, 11R29;
Secondary 11R42
MathSciNet review:
1468198
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Abstract:
It is known that there are only finitely many imaginary abelian number fields with class numbers equal to their genus class numbers. Here, we determine all the imaginary cyclic fields of  -power degrees with class numbers equal to their genus class numbers.
References:
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- S. Louboutin. Determination of all nonquadratic imaginary cyclic number fields of
 -power degrees with ideal class groups of exponents  . Math. Comp., 64 (1995), 323-340. MR 95c:11124 - [Lou2]
- S. Louboutin. A finiteness theorem for imaginary abelian number fields. Manuscripta math., 91 (1996), 343-352. MR 97f:11089
- [Lou3]
- S. Louboutin. CM-fields with cyclic ideal class groups of -power orders. J. of Nb. Th., 67 (1997), 1-10. MR 98h:11139
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- I. Miyada. On imaginary abelian number fields of type
 with one class in each genus. Manuscripta math., 88 (1995), 535-540. MR 96j:11146 - [PK]
- Y.-H. Park and S.-H. Kwon. Determination of all non-quadratic imaginary cyclic number fields of -power degree with class number
 . Acta Arith., 83 (1998), 211-223. CMP 98:09 - [Wa]
- L.C. Washington. Introduction to Cyclotomic Fields. Springer-Verlag, Grad. Texts Math. 83 (1997). MR 85g:11001
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- K. Yamamura. The determination of the imaginary abelian number fields with class-number one. Math. Comp., 62 (1994), 899-921. MR 94g:11096
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Additional Information:
Stéphane
Louboutin
Affiliation:
Université de Caen, UFR Sciences, Département de Mathématiques, 14032 Caen cedex, France
Email:
loubouti@math.unicaen.fr
DOI:
10.1090/S0002-9939-99-04548-7
PII:
S 0002-9939(99)04548-7
Keywords:
Genus field,
relative class number,
class number,
cyclic number field
Received by editor(s):
January 31, 1997
Received by editor(s) in revised form:
May 28, 1997
Communicated by:
William W. Adams
Copyright of article:
Copyright
1999,
American Mathematical Society
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