scholarly journals Hyperelliptic curves and homomorphisms to ideal class groups of quadratic number fields

2011 ◽  
Vol 131 (12) ◽  
pp. 2303-2309
Author(s):  
Tormod Kalberg Sivertsen ◽  
Ragnar Soleng
Keyword(s):  
Number Fields ◽  
Hyperelliptic Curves ◽  
Ideal Class ◽  
Quadratic Number ◽  
Class Groups ◽  
Ideal Class Groups ◽  
Quadratic Number Fields

scholarly journals Tournaments and Ideal Class Groups

1995 ◽  
Vol 38 (3) ◽  
pp. 330-333
Author(s):  
Robert J. Kingan
Keyword(s):  
Class Group ◽  
Number Fields ◽  
Ideal Class ◽  
Ideal Class Group ◽  
Quadratic Number ◽  
Class Groups ◽  
Ideal Class Groups ◽  
Quadratic Number Fields ◽  
The Ideal

AbstractResults are given for a class of square {0,1}-matrices which provide information about the 4-rank of the ideal class group of certain quadratic number fields.

scholarly journals A Note on 4-Rank Densities

2004 ◽  
Vol 47 (3) ◽  
pp. 431-438 ◽  
Author(s):  
Robert Osburn
Keyword(s):  
Number Fields ◽  
Product Formula ◽  
Ideal Class ◽  
Quadratic Number ◽  
Class Groups ◽  
Hilbert Symbol ◽  
Ideal Class Groups ◽  
Tame Kernels ◽  
Real Quadratic ◽  
Density Results

AbstractFor certain real quadratic number fields, we prove density results concerning 4-ranks of tame kernels. We also discuss a relationship between 4-ranks of tame kernels and 4-class ranks of narrow ideal class groups. Additionally, we give a product formula for a local Hilbert symbol.

Circulant Graphs and 4-Ranks of Ideal Class Groups

1994 ◽  
Vol 46 (1) ◽  
pp. 169-183 ◽  
Author(s):  
Jurgen Hurrelbrink
Keyword(s):  
Quadratic Forms ◽  
Class Group ◽  
Number Fields ◽  
Regular Graphs ◽  
Ideal Class ◽  
Ideal Class Group ◽  
Quadratic Number ◽  
Ideal Class Groups ◽  
Yield Information ◽  
The Ideal

AbstractThis is about results on certain regular graphs that yield information about the structure of the ideal class group of quadratic number fields associated with these graphs. Some of the results can be formulated in terms of the quadratic forms x2 + 27y2, x2 + 32y2, x2 + 64y2.

scholarly journals A Note on Ideal Class Groups

1966 ◽  
Vol 27 (1) ◽  
pp. 239-247 ◽  
Author(s):  
Kenkichi Iwasawa
Keyword(s):  
Class Group ◽  
Cyclotomic Field ◽  
Theoretical Method ◽  
Number Fields ◽  
Ideal Class ◽  
Ideal Class Group ◽  
Class Groups ◽  
Algebraic Number Fields ◽  
Ideal Class Groups ◽  
The Ideal

In the first part of the present paper, we shall make some simple observations on the ideal class groups of algebraic number fields, following the group-theoretical method of Tschebotarew. The applications on cyclotomic fields (Theorems 5, 6) may be of some interest. In the last section, we shall give a proof to a theorem of Kummer on the ideal class group of a cyclotomic field.

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