Solving Norm Form Equations over Number Fields (original) (raw)

Lecture Notes in Computer Science, 2009

Abstract

ABSTRACT Let K be a number field and L a finite extension of K of degree ℓ. Let ω 1 = 1,ω 2,..., ω ℓ be K-linearly independent integers of L and k an integer of K. We denote by N L/K the norm from L to K. In this paper we give an algorithm for the computation of algebraic integers, x 1,..., x ℓ ∈ K satisfying the equation N L/K (ω 1 x 1 + ⋯ + x ℓ ω ℓ) = k.

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