arXiv 1012.06752010-12math.NT

Multiplicative zero-one laws and metric number theory

Victor Beresnevich, Alan Haynes, Sanju Velani

备注：: 13 pages
发表信息：: Acta Arithmetica, 160(2), 101-114, 2013

英文摘要：

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.

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