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Euclidean Windows

Published online by Cambridge University Press:  01 February 2010

Stefania Cavallar and
Franz Lemmermeyer
Stefania Cavallar
Affiliation:
CWI, Kruislaan 413, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands, Stefania.Cavallar@cwi.nl
Franz Lemmermeyer
Affiliation:
Univ. San Marcos, Department of Mathematics, 333 South Twin Oaks Valley Road, San Marcos, CA 92096-0001, franzl@csusm.edu

Abstract

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In this paper we study number fields which are Euclidean with respect to functions that are different from the absolute value of the norm, namely weighted norms that depend on a real parameter c. We introduce the Euclidean minimum of weighted norms as the set of values of c for which the function is Euclidean, and we show that the Euclidean minimum may be irrational and not isolated. We also present computational results on Euclidean minima of cubic number fields, and present a list of norm-Euclidean complex cubic fields that we conjecture to be complete.

Information

Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 3 , 2000, pp. 336 - 355
Copyright
Copyright © London Mathematical Society 2000

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