Integral points and volume of integral-integral affine manifolds
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915798985998336 |
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| author | Elisha, Oded Karshon, Yael Loizides, Yiannis |
| author_facet | Elisha, Oded Karshon, Yael Loizides, Yiannis |
| contents | We give an elementary proof that, for a closed manifold with an integral-integral affine structure, its total volume and number of integral points coincide. The proof uses rational Ehrhart theory and elementary Fourier analysis to estimate the difference between the total volume and the number of integral points. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_17551 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Integral points and volume of integral-integral affine manifolds Elisha, Oded Karshon, Yael Loizides, Yiannis Differential Geometry Symplectic Geometry 53C15 (Primary) 52B20, 53D50 (Secondary) We give an elementary proof that, for a closed manifold with an integral-integral affine structure, its total volume and number of integral points coincide. The proof uses rational Ehrhart theory and elementary Fourier analysis to estimate the difference between the total volume and the number of integral points. |
| title | Integral points and volume of integral-integral affine manifolds |
| topic | Differential Geometry Symplectic Geometry 53C15 (Primary) 52B20, 53D50 (Secondary) |
| url | https://arxiv.org/abs/2508.17551 |