Bounds on the gaps in the fractional parts of a linear form

We provide bounds on the sizes of the gaps – defined broadly – in the set ${k_{1} β_{1} + \dots + k_{n} β_{n} (m o d 1) : k_{i} \in Z \cap (0, Q^{\frac{1}{n}}]}$ for generic $β_{1}, \dots, β_{n} \in R^{m}$ and all sufficiently large $Q$ . We also introduce a related problem in Diophantine approximation, which we believe is of independent interest.

Bounds on the gaps in the fractional parts of a linear form

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Bounds on the gaps in the fractional parts of a linear form

文献摘要

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Bounds on the gaps in the fractional parts of a linear form

文献摘要

讨论

|讲解博客

|AI智能校验

Bounds on the gaps in the fractional parts of a linear form

文献摘要

讨论

|讲解博客

|AI智能校验

讲解博客

AI智能校验

讲解博客

AI智能校验