cubic fields
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scholarly journals Elliptic curves over totally real cubic fields are modular

2020 ◽  
Vol 14 (7) ◽  
pp. 1791-1800
Author(s):  
Maarten Derickx ◽  
Filip Najman ◽  
Samir Siksek
Keyword(s):  
Elliptic Curves ◽  
Cubic Fields ◽  
Totally Real

scholarly journals On a conjecture of Lemmermeyer

2020 ◽  
Vol 16 (07) ◽  
pp. 1407-1424
Author(s):  
Siham Aouissi ◽  
Mohamed Talbi ◽  
Moulay Chrif Ismaili ◽  
Abdelmalek Azizi
Keyword(s):  
Class Groups ◽  
Root Of Unity ◽  
Cubic Fields

Let [Formula: see text] be a prime and denote by [Formula: see text] a primitive third root of unity. Recently, Lemmermeyer presented a conjecture about [Formula: see text]-class groups of pure cubic fields [Formula: see text] and of their normal closures [Formula: see text]. The main goal of this paper is to reduce Lemmermeyer’s conjecture to a problem of unit theory by showing that the conjecture of Lemmermeyer follows from Conjecture 2.9.

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