Determination of all imaginary quadratic fields for which their Hilbert 2-class fields have 2-class groups of rank 2

2021 ◽  
Author(s):  
Elliot Benjamin ◽  
C. Snyder
Keyword(s):  
Quadratic Fields ◽  
Class Groups ◽  
Imaginary Quadratic Fields ◽  
Rank 2 ◽  
Class Fields

scholarly journals On the Schertz Conjecture

2019 ◽  
Vol 62 (3) ◽  
pp. 837-845
Author(s):  
Ja Kyung Koo ◽  
Dong Sung Yoon
Keyword(s):  
Abelian Extension ◽  
Quadratic Fields ◽  
Class Groups ◽  
Imaginary Quadratic Fields ◽  
Limit Formula ◽  
Kronecker Limit Formula

AbstractSchertz conjectured that every finite abelian extension of imaginary quadratic fields can be generated by the norm of the Siegel–Ramachandra invariants. We present a conditional proof of his conjecture by means of the characters on class groups and the second Kronecker limit formula.

Completely normal elements in some finite abelian extensions

2013 ◽  
Vol 11 (10) ◽  
Author(s):  
Ja Koo ◽  
Dong Shin
Keyword(s):  
Function Fields ◽  
Modular Function ◽  
Rational Numbers ◽  
Quadratic Fields ◽  
Cyclotomic Fields ◽  
Imaginary Quadratic Fields ◽  
Abelian Extensions ◽  
Class Fields ◽  
Normal Element ◽  
Ray Class Fields

AbstractWe present some completely normal elements in the maximal real subfields of cyclotomic fields over the field of rational numbers, relying on the criterion for normal element developed in [Jung H.Y., Koo J.K., Shin D.H., Normal bases of ray class fields over imaginary quadratic fields, Math. Z., 2012, 271(1–2), 109–116]. And, we further find completely normal elements in certain abelian extensions of modular function fields in terms of Siegel functions.

Sign in / Sign up

Export Citation Format

Share Document