Khintchine's theorem for affine hyperplanes in positive charateristic

Arijit Ganguly

doi:10.1016/j.jnt.2021.08.001

Khintchine's theorem for affine hyperplanes in positive charateristic

Arijit Ganguly

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper we establish the convergence case of Khintchine's theorem for affine hyperplanes in function field of positive characteristic. Along with that, we also prove a quantitative version of the same. The main technique used in the proof is a dynamical result called ‘Quantitative nondivergence’ due to D.Y. Kleinbock and G.A. Margulis ([23]).

Original language	English
Pages (from-to)	17-36
Number of pages	20
Journal	Journal of Number Theory
Volume	238
DOIs	https://doi.org/10.1016/j.jnt.2021.08.001
State	Published - Sep 2022
Externally published	Yes

Keywords

Diophantine approximation
Dynamical systems

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10.1016/j.jnt.2021.08.001

Cite this

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title = "Khintchine's theorem for affine hyperplanes in positive charateristic",

abstract = "In this paper we establish the convergence case of Khintchine's theorem for affine hyperplanes in function field of positive characteristic. Along with that, we also prove a quantitative version of the same. The main technique used in the proof is a dynamical result called {\textquoteleft}Quantitative nondivergence{\textquoteright} due to D.Y. Kleinbock and G.A. Margulis ([23]).",

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note = "Publisher Copyright: {\textcopyright} 2021 Elsevier Inc.",

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AB - In this paper we establish the convergence case of Khintchine's theorem for affine hyperplanes in function field of positive characteristic. Along with that, we also prove a quantitative version of the same. The main technique used in the proof is a dynamical result called ‘Quantitative nondivergence’ due to D.Y. Kleinbock and G.A. Margulis ([23]).

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KW - Dynamical systems

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Khintchine's theorem for affine hyperplanes in positive charateristic

Abstract

Keywords

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