scholarly journals Heuristics for 2-class Towers of Cyclic Cubic Fields

2021 ◽  
pp. 1-12
Author(s):  
Nigel Boston ◽  
Michael R. Bush
Keyword(s):  
Cubic Fields ◽  
Cyclic Cubic Fields

scholarly journals Cyclic Cubic Fields of Given Conductor and Given Index

2006 ◽  
Vol 49 (3) ◽  
pp. 472-480 ◽  
Author(s):  
Alan K. Silvester ◽  
Blair K. Spearman ◽  
Kenneth S. Williams
Keyword(s):  
Cubic Fields ◽  
Cyclic Cubic Fields

AbstractThe number of cyclic cubic fields with a given conductor and a given index is determined.

scholarly journals Torsion of elliptic curves over cyclic cubic fields

2018 ◽  
Vol 88 (319) ◽  
pp. 2443-2459 ◽  
Author(s):  
Maarten Derickx ◽  
Filip Najman
Keyword(s):  
Elliptic Curves ◽  
Cubic Fields ◽  
Cyclic Cubic Fields

scholarly journals The size function for cyclic cubic fields

2018 ◽  
Vol 14 (02) ◽  
pp. 399-415
Author(s):  
Ha Thanh Nguyen Tran ◽  
Peng Tian
Keyword(s):  
Number Field ◽  
Algebraic Curve ◽  
Number Fields ◽  
Size Function ◽  
Rank One ◽  
Cubic Fields ◽  
Cyclic Cubic Fields

The size function for a number field is an analogue of the dimension of the Riemann–Roch spaces of divisors on an algebraic curve. It was conjectured to attain its maximum at the trivial class of Arakelov divisors. This conjecture was proved for many number fields with unit groups of rank one. Our research confirms that the conjecture also holds for cyclic cubic fields, which have unit groups of rank two.

Sign in / Sign up

Export Citation Format

Share Document