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ZERO-ONE LAWS IN SIMULTANEOUS AND MULTIPLICATIVE DIOPHANTINE APPROXIMATION

Part of: Diophantine approximation, transcendental number theory

Published online by Cambridge University Press:  21 January 2013

Liangpan Li
Liangpan Li*
Affiliation:
Department of Mathematical Sciences, Loughborough University, Loughborough LE11 3TU, U.K. (email: liliangpan@gmail.com)

Abstract

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Answering two questions of Beresnevich and Velani, we develop zero-one laws in both simultaneous and multiplicative Diophantine approximation. Our proofs mainly rely on a versatile Cassels–Gallagher type theorem and the cross fibering principle of Beresnevich, Haynes and Velani.

MSC classification

Secondary: 11J13: Simultaneous homogeneous approximation, linear forms 11J83: Metric theory

Information

Type
Research Article
Information
Mathematika , Volume 59 , Issue 2 , July 2013 , pp. 321 - 332
Copyright
Copyright © 2013 University College London 

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