scholarly journals Improvements in the computation of ideal class groups of imaginary quadratic number fields

2010 ◽  
Vol 4 (2) ◽  
pp. 141-154 ◽  
Author(s):  
Jean-François Biasse
Keyword(s):  
Number Fields ◽  
Ideal Class ◽  
Quadratic Number ◽  
Class Groups ◽  
Ideal Class Groups ◽  
Quadratic Number Fields ◽  
Imaginary Quadratic Number

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 GLOBAL UNITS MODULO ELLIPTIC UNITS AND IDEAL CLASS GROUPS

2012 ◽  
Vol 08 (03) ◽  
pp. 569-588
Author(s):  
STÉPHANE VIGUIÉ
Keyword(s):  
Class Group ◽  
Finite Extension ◽  
Projective Limit ◽  
Ideal Class ◽  
Quadratic Number ◽  
Class Groups ◽  
Quadratic Number Field ◽  
Ideal Class Groups ◽  
Imaginary Quadratic Number ◽  
Elliptic Units

Let p be a prime number, and let k be an imaginary quadratic number field in which p decomposes into two distinct primes 𝔭 and [Formula: see text]. Let k∞ be the unique ℤp-extension of k which is unramified outside of 𝔭, and let K∞ be a finite extension of k∞, abelian over k. Following closely the ideas of Belliard in [1], we prove that in K∞, the projective limit of the p-class group and the projective limit of units modulo elliptic units share the same μ-invariant and the same λ-invariant. We deduce that a version of the classical main conjecture, which is known to be true for p ∉ {2, 3}, holds also for p ∈ {2, 3} once we neglect the μ-invariants.

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.

scholarly journals Imaginary quadratic number fields with class groups of small exponent

2020 ◽  
Vol 193 (3) ◽  
pp. 217-233
Author(s):  
Andreas-Stephan Elsenhans ◽  
Jürgen Klüners ◽  
Florin Nicolae
Keyword(s):  
Number Fields ◽  
Quadratic Number ◽  
Class Groups ◽  
Quadratic Number Fields ◽  
Imaginary Quadratic Number
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