Multiplicative zero-one laws and metric number theory

• Autorzy: Victor Beresnevich , Alan Haynes , Sanju Velani
• Języki publikacji: EN

Abstrakty

EN

We develop the classical theory of Diophantine approximation without assuming monotonicity or convexity. A complete 'multiplicative' zero-one law is established akin to the 'simultaneous' zero-one laws of Cassels and Gallagher. As a consequence we are able to establish the analogue of the Duffin-Schaeffer theorem within the multiplicative setup. The key ingredient is the rather simple but nevertheless versatile 'cross fibering principle'. In a nutshell it enables us to 'lift' zero-one laws to higher dimensions.

Kategorie tematyczne

• 11K60: Diophantine approximation
• 11J83: Metric theory
• 11J13: Simultaneous homogeneous approximation, linear forms

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2013
• Tom: 160
• Numer: 2
• Strony: 101-114

Daty

wydano

2013

Twórcy

autor

Victor Beresnevich

• Department of Mathematics, University of York, Heslington, York, YO10 5DD, England

autor

Alan Haynes

• Department of Mathematics, University of York, Heslington, York, YO10 5DD, England

autor

Sanju Velani

• Department of Mathematics, University of York, Heslington, York, YO10 5DD, England

Identyfikatory

DOI

10.4064/aa160-2-1