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AbstractIn 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 parameterc. We introduce the Euclidean minimum of weighted norms as the set of values ofcfor 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 ofdoi:10.1112/s1461157000000334 fatcat:ohb3eer3rnbb5ckwqujloza44i