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On the S-Euclidean minimum of an ideal class

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McGown K.

Acta Arithmetica

2015

tom 171

nr 2

125-144

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.

Ograniczanie wyników

1 Acta Arithmetica

1 McGown K.

1 2015

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On the S-Euclidean minimum of an ideal class