Multiplicative zero-one laws and metric number theory

Victor 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 -