# Multiplicative zero-one laws and metric number theory

Victor Beresnevich; Alan Haynes; Sanju Velani

Acta Arithmetica (2013)

- Volume: 160, Issue: 2, page 101-114
- ISSN: 0065-1036

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topVictor Beresnevich, Alan Haynes, and Sanju Velani. "Multiplicative zero-one laws and metric number theory." Acta Arithmetica 160.2 (2013): 101-114. <http://eudml.org/doc/279708>.

@article{VictorBeresnevich2013,

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.},

author = {Victor Beresnevich, Alan Haynes, Sanju Velani},

journal = {Acta Arithmetica},

keywords = {zero-one law; metric multiplicative diophantine approximation; Duffin–Schaeffer theorem},

language = {eng},

number = {2},

pages = {101-114},

title = {Multiplicative zero-one laws and metric number theory},

url = {http://eudml.org/doc/279708},

volume = {160},

year = {2013},

}

TY - JOUR

AU - Victor Beresnevich

AU - Alan Haynes

AU - Sanju Velani

TI - Multiplicative zero-one laws and metric number theory

JO - Acta Arithmetica

PY - 2013

VL - 160

IS - 2

SP - 101

EP - 114

AB - 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.

LA - eng

KW - zero-one law; metric multiplicative diophantine approximation; Duffin–Schaeffer theorem

UR - http://eudml.org/doc/279708

ER -

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