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Abstract
In this paper we prove an upper bound on the "size" of the set of multiplicatively ψapproximable points in R^d for d>1 in terms of fdimensional Hausdorff measure. This upper bound exactly complements the known lower bound, providing a "zerofull" law which relates the Hausdorff measure to the convergence/divergence of a certain series in both the homogeneous and inhomogeneous settings. This zerofull law resolves a question posed by Beresnevich and Velani (2015) regarding the "log factor" discrepancy in the convergent/divergent sum conditions of their theorem. We further prove the analogous result for the multiplicative doubly metric setup.
Original language  English 

Number of pages  10 
Publication status  Submitted  1 Dec 2016 
Projects
 1 Finished

Programme GrantNew Frameworks in metric Number Theory
1/06/12 → 30/11/18
Project: Research project (funded) › Research