The Memoirs of the AMS is devoted to the publication of new research in all areas of pure and applied mathematics. The Memoirs is designed particularly to publish long papers of groups of cognate papers in book form, and is under the supervision of the Editorial Committee of the AMS journal Transactions of the American Mathematical Society. All papers are peer-reviewed.
1. Introduction
2. Preliminaries
3. A fully inhomogeneous version of Gallagher's theorem
4. Liouville fibres
5. Obstructions on Liouville fibres
A. Pathology
Sam Chow, University of Warwick, Coventry, United Kingdom, and Niclas Technau, Max Planck Institute for Mathematics, Bonn, Germany.
