Exponential valuations on lattice polygons
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866908370844254208 |
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| author | Boroczky, Karoly J. Domokos, Matyas Freyer, Ansgar Haberl, Christoph Harcos, Gergely li, Jin |
| author_facet | Boroczky, Karoly J. Domokos, Matyas Freyer, Ansgar Haberl, Christoph Harcos, Gergely li, Jin |
| contents | We classify translatively exponential and GL(2,Z) covariant valuations on lattice polygons valued at measurable real functions. A typical example of such valuations is induced by the Laplace transform, but as it turns out there are many more. The argument uses the ergodicity of the linear action of SL(2,Z) on R2, and some elementary properties of the Fibonacci numbers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_09383 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Exponential valuations on lattice polygons Boroczky, Karoly J. Domokos, Matyas Freyer, Ansgar Haberl, Christoph Harcos, Gergely li, Jin Number Theory We classify translatively exponential and GL(2,Z) covariant valuations on lattice polygons valued at measurable real functions. A typical example of such valuations is induced by the Laplace transform, but as it turns out there are many more. The argument uses the ergodicity of the linear action of SL(2,Z) on R2, and some elementary properties of the Fibonacci numbers. |
| title | Exponential valuations on lattice polygons |
| topic | Number Theory |
| url | https://arxiv.org/abs/2411.09383 |