Fully Inhomogeneous Multiplicative Diophantine Approximation of Badly Approximable Numbers

Sam Chow; Agamemnon Zafeiropoulos

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arXiv · 2103.03605

Fully Inhomogeneous Multiplicative Diophantine Approximation of Badly Approximable Numbers

Sam Chow·Agamemnon Zafeiropoulos

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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.

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Sam Chow, Agamemnon Zafeiropoulos. 2021-03-05. Fully Inhomogeneous Multiplicative Diophantine Approximation of Badly Approximable Numbers. https://arxiv.org/abs/2103.03605

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