Values of inhomogeneous forms at
            <i>S</i>
            ‐integral points

Ghosh, Anish; Han, Jiyoung

doi:10.1112/mtk.12137

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2022

2023

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Cited by 3 publications

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“…[7, Theorem 5.2]). Let d ≥ 3 and let E = p∈S E p be the product of bounded Borel sets E p ⊆ Q d p for p ∈ S. There is a constant C d > 0, depending only on the dimension d, such that…”

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confidence: 99%

A quantitative Khintchine-Groshev theorem for S-arithmetic Diophantine approximation

Han¹

2022

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In [18], Schmidt studied a quantitative type of Khintchine-Groshev theorem. Recently, a new proof of the theorem was found, which made it possible to relax the dimensional constraint and more generally, to add on the congruence condition [1].In this paper, we generalize this new approach to S-arithmetic spaces and obtain a quantitative version of an S-arithmetic Khintchine-Groshev theorem. In fact, we consider a new S-arithmetic analog of Diophantine approximation, which is different from the one formerly established (see [15]). Hence for the sake of completeness, we also deal with the convergence case of the Khintchine-Groshev theorem, based on this new generalization.

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confidence: 99%