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• W2915489697 abstract "We prove over fields of power series the analogues of several Diophantine approximation results obtained over the field of real numbers. In particular we establish the power series analogue of Kronecker's theorem for matrices, together with a quantitative form of it, which can also be seen as a transference inequality between uniform approximation and inhomogeneous approximation. Special attention is devoted to the one dimensional case. Namely, we give a necessary and sufficient condition on an irrational power series $alpha$ which ensures that, for some positive $eps$, the set $$ liminf_{Q in mathbb{F}_q[z], ,, deg Q to infty} | Q | cdot |langle Q alpha - theta rangle| geq eps $$ has full Hausdorff dimension." @default.
• W2915489697 created "2019-03-02" @default.
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• W2915489697 date "2019-11-27" @default.
• W2915489697 modified "2023-10-16" @default.
• W2915489697 title "On homogeneous and inhomogeneous Diophantine approximation over the fields of formal power series" @default.
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• W2915489697 doi "https://doi.org/10.2140/pjm.2019.302.453" @default.
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