Effective multi-equidistribution for translates of unipotent flows and Central limit theorems in inhomogeneous Diophantine approximation
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866913080368168960 |
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| author | Aggarwal, Gaurav Das, Sourav Ghosh, Anish |
| author_facet | Aggarwal, Gaurav Das, Sourav Ghosh, Anish |
| contents | In this paper, we prove a central limit theorem for inhomogeneous Diophantine approximation with a fixed shift, provided the shift is non-Liouville. This generalizes earlier work of Dolgopyat, Fayad, and Vinogradov~\cite{DFV}. This is achieved by translating the problem to one involving flows on homogeneous spaces. In this latter setting, we establish an effective multi-equidistribution result for diagonal translates of unipotent flows. This result is obtained by combining a recent result of Kim~\cite{Kim2024} with the height function construction of Shi~\cite{Shi20}. The central limit theorem is then deduced using the method of Björklund and Gorodnik~\cite{BG}. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_00507 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Effective multi-equidistribution for translates of unipotent flows and Central limit theorems in inhomogeneous Diophantine approximation Aggarwal, Gaurav Das, Sourav Ghosh, Anish Number Theory Dynamical Systems Probability Primary: 11K60, Secondary: 60F05, 37A17 In this paper, we prove a central limit theorem for inhomogeneous Diophantine approximation with a fixed shift, provided the shift is non-Liouville. This generalizes earlier work of Dolgopyat, Fayad, and Vinogradov~\cite{DFV}. This is achieved by translating the problem to one involving flows on homogeneous spaces. In this latter setting, we establish an effective multi-equidistribution result for diagonal translates of unipotent flows. This result is obtained by combining a recent result of Kim~\cite{Kim2024} with the height function construction of Shi~\cite{Shi20}. The central limit theorem is then deduced using the method of Björklund and Gorodnik~\cite{BG}. |
| title | Effective multi-equidistribution for translates of unipotent flows and Central limit theorems in inhomogeneous Diophantine approximation |
| topic | Number Theory Dynamical Systems Probability Primary: 11K60, Secondary: 60F05, 37A17 |
| url | https://arxiv.org/abs/2605.00507 |