scholarly journals A construction of normal bases over the Hilbert $p$-class field of imaginary quadratic fields

1998 ◽  
Vol 74 (1) ◽  
pp. 25-28
Author(s):  
Tsuyoshi Itoh
Keyword(s):  
Quadratic Fields ◽  
Imaginary Quadratic Fields ◽  
Class Field ◽  
Normal Bases

Class field towers of imaginary quadratic fields

1987 ◽  
Vol 57 (4) ◽  
pp. 425-450 ◽  
Author(s):  
James R. Brink ◽  
Robert Gold
Keyword(s):  
Quadratic Fields ◽  
Imaginary Quadratic Fields ◽  
Class Field ◽  
Class Field Towers

scholarly journals Normal bases of ray class fields over imaginary quadratic fields

2011 ◽  
Vol 271 (1-2) ◽  
pp. 109-116 ◽  
Author(s):  
Ho Yun Jung ◽  
Ja Kyung Koo ◽  
Dong Hwa Shin
Keyword(s):  
Quadratic Fields ◽  
Imaginary Quadratic Fields ◽  
Normal Bases ◽  
Class Fields ◽  
Ray Class 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.

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