Equidistribution in 2-Nilpotent Polish Groups and triple restricted sumsets
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866918392478302208 |
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| author | Ackelsberg, Ethan Jamneshan, Asgar |
| author_facet | Ackelsberg, Ethan Jamneshan, Asgar |
| contents | The aim of this paper is to establish a Ratner-type equidistribution theorem for orbits on homogeneous spaces associated with 2-nilpotent locally compact Polish groups under the action of a countable discrete abelian group. We apply this result to establish the existence of triple restricted sumsets in subsets of positive density in arbitrary countable discrete abelian groups, subject to a necessary finiteness condition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_07865 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Equidistribution in 2-Nilpotent Polish Groups and triple restricted sumsets Ackelsberg, Ethan Jamneshan, Asgar Dynamical Systems Combinatorics Primary 11B13, 37A15, Secondary 11B30, 22F30 The aim of this paper is to establish a Ratner-type equidistribution theorem for orbits on homogeneous spaces associated with 2-nilpotent locally compact Polish groups under the action of a countable discrete abelian group. We apply this result to establish the existence of triple restricted sumsets in subsets of positive density in arbitrary countable discrete abelian groups, subject to a necessary finiteness condition. |
| title | Equidistribution in 2-Nilpotent Polish Groups and triple restricted sumsets |
| topic | Dynamical Systems Combinatorics Primary 11B13, 37A15, Secondary 11B30, 22F30 |
| url | https://arxiv.org/abs/2504.07865 |