A significant portion of MacMahon’s famous book “Combinatory Analysis” is devoted to the development of “Partition Analysis” as a computational method for solving problems in connection with linear homogeneous diophantine inequalities and equations, respectively. Nevertheless, MacMahon’s ideas have not received due attention with the exception of work by Richard Stanley. A long range object of ...

In this paper we establish a general form of the Mass Transference Principle for systems of linear forms conjectured in [1]. We also present a number of applications to problems in Diophantine approximation. These include a general transference of Khintchine–Groshev type theorems into Hausdorff measure statements. These statements are applicable in both the homogeneous and inhomogeneous setting...

The main objective of this paper is to prove a Khintchine type theorem on divergence of linear Diophantine approximation on nondegenerate manifolds, which completes earlier results for convergence. 2000 Math. Subj. Class. Primary 11J83; Secondary 11K60.