Littlewood and Duffin--Schaeffer-type problems in diophantine approximation

Abstract

Gallagher's theorem describes the multiplicative diophantine approximation rate of a typical vector. We establish a fully-inhomogeneous version of Gallagher's theorem, a diophantine fibre refinement, and a sharp and unexpected threshold for Liouville fibres. Along the way, we prove an inhomogeneous version of the Duffin--Schaeffer conjecture for a class of non-monotonic approximation functions.

83 pages; to appear in the Memoirs of the American Mathematical Society

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