On the S-Euclidean minimum of an ideal class

• Autorzy: Kevin J. McGown
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 54H20: Topological dynamics
• 11R04: Algebraic numbers; rings of algebraic integers
• 22D40: Ergodic theory on groups
• 11H55: Quadratic forms (reduction theory, extreme forms, etc.)
• 13F07: Euclidean rings and generalizations
• 11H50: Minima of forms

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2015
• Tom: 171
• Numer: 2
• Strony: 125-144

Daty

wydano

2015

Twórcy

autor

Kevin J. McGown

• Department of Mathematics and Statistics, California State University, Chico, 400 West First Street, Chico, CA 95929, U.S.A.

Identyfikatory

DOI

10.4064/aa171-2-2