Comptage asymptotique et algorithmique d'extensions cubiques relatives

Anna Morra 1, 2
2 LFANT - Lithe and fast algorithmic number theory
IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest
Abstract : This thesis deals with counting relative cubic extensions. In the first chapter we describe a joint work with Henri Cohen. Let k be a number field. We give an asymptotic formula for the number of isomorphism classes of cubic extensions L/k such that the Galois closure of L/k contains a fixed quadratic extension K_2/k. The main tool is Kummer theory. In the second chapter, we suppose k to be an imaginary quadratic number field (with class number 1) and we describe an algorithm for listing all isomorphism classes of cubic extensions L/k up to a bound X on the norm of the relative discriminant ideal.
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Anna Morra. Comptage asymptotique et algorithmique d'extensions cubiques relatives. Mathématiques [math]. Université Bordeaux 1, 2009. Français. ⟨tel-00525320⟩

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