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Multiplicative zero-one laws and metric number theory

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JournalActa Arithmetica
DateE-pub ahead of print - 3 Dec 2010
DatePublished (current) - Jun 2013
Issue number2
Volume160
Number of pages14
Pages (from-to)101-114
Early online date3/12/10
Original languageEnglish

Abstract

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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    Research areas

  • Diophantine approximation, zero-one laws, Duffin-Schaeffer conjecture

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