کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
6415584 1630677 2014 29 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Remarks on Euclidean minima
ترجمه فارسی عنوان
اظهار نظر در مورد مینیمیا آکادمی اقلیدس؟
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
چکیده انگلیسی

The Euclidean minimum M(K) 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 M(K), as the supremum in the Euclidean spectrum Spec(K), is isolated and attained and can be computed in finite time. We extend Cerriʼs 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, M(K) is isolated and attained and Cerriʼs algorithm computes M(K) in finite time.(2)If K is a non-CM field of unit rank 2 or higher, then the computational complexity of M(K) is bounded in terms of the degree, discriminant and regulator of K.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Number Theory - Volume 137, April 2014, Pages 93-121
نویسندگان
, ,