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We introduce the Euclidean minimum of weighted norms as the set of values of <jats:italic>c<\/jats:italic> 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.<\/jats:p>","DOI":"10.1112\/s1461157000000334","type":"journal-article","created":{"date-parts":[[2010,10,21]],"date-time":"2010-10-21T15:24:58Z","timestamp":1287674698000},"page":"336-355","source":"Crossref","is-referenced-by-count":1,"title":["Euclidean Windows"],"prefix":"10.1112","volume":"3","author":[{"given":"Stefania","family":"Cavallar","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Franz","family":"Lemmermeyer","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2010,2,1]]},"reference":[{"key":"S1461157000000334_ref003","first-page":"28","article-title":"\u2018A Euclidean ring containing \u2124[\u221a14]\u2019","volume":"19","author":"Cardon","year":"1997","journal-title":"C. 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