On the asymptotic behaviour of the ideal counting function in quadratic number fields

1989 ◽  
Vol 108 (4) ◽  
pp. 301-323 ◽  
Author(s):  
Wolfgang M�ller
Keyword(s):  
Asymptotic Behaviour ◽  
Counting Function ◽  
Number Fields ◽  
Quadratic Number ◽  
Quadratic Number Fields ◽  
Ideal Counting Function ◽  
The Ideal

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 Hyperbolic tessellations and generators of for imaginary quadratic fields

2021 ◽  
Vol 9 ◽  
Author(s):  
David Burns ◽  
Rob de Jeu ◽  
Herbert Gangl ◽  
Alexander D. Rahm ◽  
Dan Yasaki
Keyword(s):  
Number Field ◽  
Number Fields ◽  
Quadratic Fields ◽  
Quadratic Number ◽  
Imaginary Quadratic Fields ◽  
Quadratic Number Fields ◽  
Formula Group ◽  
Imaginary Quadratic Number ◽  
Direct Calculations

Abstract We develop methods for constructing explicit generators, modulo torsion, of the $K_3$ -groups of imaginary quadratic number fields. These methods are based on either tessellations of hyperbolic $3$ -space or on direct calculations in suitable pre-Bloch groups and lead to the very first proven examples of explicit generators, modulo torsion, of any infinite $K_3$ -group of a number field. As part of this approach, we make several improvements to the theory of Bloch groups for $ K_3 $ of any field, predict the precise power of $2$ that should occur in the Lichtenbaum conjecture at $ -1 $ and prove that this prediction is valid for all abelian number fields.

scholarly journals On quaternion algebras over the composite of quadratic number fields

2021 ◽  
Vol 56 (1) ◽  
pp. 63-78
Author(s):  
Vincenzo Acciaro ◽  
◽  
Diana Savin ◽  
Mohammed Taous ◽  
Abdelkader Zekhnini ◽  
...  
Keyword(s):  
Number Fields ◽  
Complete Characterization ◽  
Quadratic Number ◽  
Quaternion Algebras ◽  
Quadratic Number Fields

Let p and q be two positive prime integers. In this paper we obtain a complete characterization of division quaternion algebras HK(p, q) over the composite K of n quadratic number fields.

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