Geodesic
Multiplicative zero-one laws and metric number theory
Victor Beresnevich 1   ; Alan Haynes 1   ; Sanju Velani 1
1 Department of Mathematics University of York Heslington, York, YO10 5DD, England
Acta Arithmetica, Tome 160 (2013) no. 2, pp. 101-114 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/aa160-2-1
Keywords: develop classical theory diophantine approximation without assuming monotonicity convexity complete multiplicative zero one law established akin simultaneous zero one laws cassels gallagher consequence able establish analogue duffin schaeffer theorem within multiplicative setup key ingredient rather simple nevertheless versatile cross fibering principle nutshell enables lift zero one laws higher dimensions

Victor Beresnevich  1   ; Alan Haynes  1   ; Sanju Velani  1

1 Department of Mathematics University of York Heslington, York, YO10 5DD, England 
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Victor Beresnevich; Alan Haynes; Sanju Velani. Multiplicative zero-one laws and metric number theory. Acta Arithmetica, Tome 160 (2013) no. 2, pp. 101-114. doi: 10.4064/aa160-2-1

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