Geodesic
On the $S$-Euclidean minimum of an ideal class
Kevin J. McGown1
1 Department of Mathematics and Statistics California State University, Chico 400 West First Street Chico, CA 95929, U.S.A.
Acta Arithmetica, Tome 171 (2015) no. 2, pp. 125-144.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We show that the $S$-Euclidean minimum of an ideal class is a rational number, generalizing a result of Cerri. In the proof, we actually obtain a slight refinement of this and give some corollaries which explain the relationship of our results with Lenstra's notion of a norm-Euclidean ideal class and the conjecture of Barnes and Swinnerton-Dyer on quadratic forms. In particular, we resolve a conjecture of Lenstra except when the $S$-units have rank one. The proof is self-contained but uses ideas from ergodic theory and topological dynamics, particularly those of Berend.
DOI : 10.4064/aa171-2-2
Keywords: s euclidean minimum ideal class rational number generalizing result cerri proof actually obtain slight refinement corollaries which explain relationship results lenstras notion norm euclidean ideal class conjecture barnes swinnerton dyer quadratic forms particular resolve conjecture lenstra except s units have rank proof self contained uses ideas ergodic theory topological dynamics particularly those berend

Kevin J. McGown 1

1 Department of Mathematics and Statistics California State University, Chico 400 West First Street Chico, CA 95929, U.S.A. 
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Kevin J. McGown. On the $S$-Euclidean minimum of an ideal class. Acta Arithmetica, Tome 171 (2015) no. 2, pp. 125-144. doi : 10.4064/aa171-2-2. http://geodesic.mathdoc.fr/articles/10.4064/aa171-2-2/

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