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We investigate $S$-arithmetic inhomogeneous Khintchine type theorems in the dual setting for nondegenerate manifolds. We prove the convergence case of the theorem, including, in particular, the $S$-arithmetic inhomogeneous counterpart of… Click to show full abstract
We investigate $S$-arithmetic inhomogeneous Khintchine type theorems in the dual setting for nondegenerate manifolds. We prove the convergence case of the theorem, including, in particular, the $S$-arithmetic inhomogeneous counterpart of the Baker-Sprind\v{z}uk conjectures. The divergence case is proved for $\mathbb{Q}_p$ but in the more general context of Hausdorff measures. This answers a question posed by Badziahin, Beresnevich and Velani.
Keywords:
diophantine approximation;
approximation manifolds;
arithmetic inhomogeneous;
inhomogeneous diophantine
Journal Title: Advances in Mathematics
Year Published: 2022
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Journal Title: Advances in Mathematics
Year Published: 2022
Link to full text (if available)
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recommendations!