Vasiliy Neckrasov

Winning property of counterexamples to Uniform Littlewood's Conjecture

In this paper, we prove that the set of counterexamples to the uniform Littlewood's conjecture proposed in Bandi-Fregoli-Kleinbock, that is, the set of pairs of real numbers $(x,y)$ satisfying $$ \limsup_{Q\to +\infty}\ Q\cdot \min_{1\leq q\leq Q}\langle qx\rangle\langle qy\rangle>0, $$ is hyperplane absolute winning....