A NOTE ON MATRIX APPROXIMATION IN THE THEORY OF MULTIPLICATIVE DIOPHANTINE APPROXIMATION

摘要

We prove the Hausdorff measure version of the matrix form of Gallagher's theorem in the inhomogeneous setting, thereby proving a conjecture posed by Hussain and Simmons ['The Hausdorff measure version of Gallagher's theorem-closing the gap and beyond', J. Number Theory 186 (2018), 211-225].