Remarks on Euclidean minima

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• 作者：Uri Shapira ; Zhiren Wang
• 关键词：11R21 ; 11K60 ; 11Y40 ; 37A45
• 刊名：Journal of Number Theory
• 出版年：April, 2014
• 年：2014
• 卷：137
• 期：Complete
• 页码：93-121
• 全文大小：432 K

文摘

The Euclidean minimum of a number field K is an important numerical invariant that indicates whether K is norm-Euclidean. When K is a non-CM field of unit rank 2 or higher, Cerri showed , as the supremum in the Euclidean spectrum , is isolated and attained and can be computed in finite time. We extend Cerri始s works by applying recent dynamical results of Lindenstrauss and Wang. In particular, the following facts are proved:

(1)

For any number field K of unit rank 3 or higher, is isolated and attained and Cerri始s algorithm computes in finite time.

(2)

If K is a non-CM field of unit rank 2 or higher, then the computational complexity of is bounded in terms of the degree, discriminant and regulator of K.