scholarly journals The characterization of cyclic cubic fields with power integral bases

2021 ◽  
Vol 44 (2) ◽  
Author(s):  
Tomokazu Kashio ◽  
Ryutaro Sekigawa
Keyword(s):  
Integral Bases ◽  
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 Unramified 3-extensions over cyclic cubic fields

2007 ◽  
Vol 230 (1) ◽  
pp. 167-183
Author(s):  
Akito Nomura
Keyword(s):  
Cubic Fields ◽  
Cyclic Cubic Fields

scholarly journals Elliptic curves with a point of order $13$ defined over cyclic cubic fields

2021 ◽  
Vol -1 (-1) ◽  
Author(s):  
Peter Bruin ◽  
Maarten Derickx ◽  
Michael Stoll
Keyword(s):  
Elliptic Curves ◽  
Cubic Fields ◽  
Cyclic Cubic Fields

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 Computing all power integral bases of cubic fields

1989 ◽  
Vol 53 (188) ◽  
pp. 689-689
Author(s):  
I. Ga{ál ◽  
N. Schulte
Keyword(s):  
Integral Bases ◽  
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.

Computing All Power Integral Bases of Cubic Fields

1989 ◽  
Vol 53 (188) ◽  
pp. 689 ◽  
Author(s):  
I. Gaal ◽  
N. Schulte
Keyword(s):  
Integral Bases ◽  
Cubic Fields
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