Euclidean windows
Stefania Cavallar and Franz Lemmermeyer
Abstract: 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.
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