Euclidean minima of totally real number fields: Algorithmic determination

Cerri, Jean-Paul

doi:10.1090/S0025-5718-07-01932-1

Euclidean minima of totally real number fields: Algorithmic determination
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Math. Comp. 76 (2007), 1547-1575 Request permission

Abstract:

This article deals with the determination of the Euclidean minimum $M(K)$ of a totally real number field $K$ of degree $n\geq 2$, using techniques from the geometry of numbers. Our improvements of existing algorithms allow us to compute Euclidean minima for fields of degree $2$ to $8$ and small discriminants, most of which were previously unknown. Tables are given at the end of this paper.

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