scholarly journals From Picard groups of hyperelliptic curves to class groups of quadratic fields

2020 ◽  
pp. 1
Author(s):  
Jean Gillibert
Keyword(s):  
Hyperelliptic Curves ◽  
Quadratic Fields ◽  
Class Groups ◽  
Picard Groups

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.

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