Zero-one laws in simultaneous and multiplicative Diophantine approximation

Abstract

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

References in corpus (3)

• An Inhomogeneous Transference Principle and Diophantine Approximation
• A note on zero-one laws in metrical Diophantine approximation
• Classical metric Diophantine approximation revisited

Cited by in corpus (1)

• The Duffin-Schaeffer type conjectures in various local fields