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Fully Inhomogeneous Multiplicative Diophantine Approximation of Badly Approximable Numbers (2103.03605v2)
Published 5 Mar 2021 in math.NT
Abstract: We establish a strong form of Littlewood's conjecture with inhomogeneous shifts, for a full-dimensional set of pairs of badly approximable numbers on a vertical line. We also prove a uniform assertion of this nature, generalising a strong form of a result by Haynes, Jensen and Kristensen. Finally, we establish a similar result involving inhomogeneously badly approximable numbers, making progress towards a problem posed by Pollington, Velani, Zafeiropoulos and Zorin.