Heights, regulators and Schinzel's determinant inequality

• Autorzy: Shabnam Akhtari , Jeffrey D. Vaaler
• Języki publikacji: EN

Abstrakty

EN

We prove inequalities that compare the size of an S-regulator with a product of heights of multiplicatively independent S-units. Our upper bound for the S-regulator follows from a general upper bound for the determinant of a real matrix proved by Schinzel. The lower bound for the S-regulator follows from Minkowski's theorem on successive minima and a volume formula proved by Meyer and Pajor. We establish similar upper bounds for the relative regulator of an extension l/k of number fields.

Kategorie tematyczne

• 11R04: Algebraic numbers; rings of algebraic integers
• 11J25: Diophantine inequalities
• 46B04: Isometric theory of Banach spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2016
• Tom: 172
• Numer: 3
• Strony: 285-298

Daty

wydano

2016

Twórcy

autor

Shabnam Akhtari

• Department of Mathematics, University of Oregon, Eugene, OR 97403, U.S.A.

autor

Jeffrey D. Vaaler

• Department of Mathematics, University of Texas, Austin, TX 78712, U.S.A.

Identyfikatory

DOI

10.4064/aa8253-1-2016