Motivic Mellin transforms
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917877503754240 |
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| author | Cluckers, Raf Loeser, François Nguyen, Kien Huu Vermeulen, Floris |
| author_facet | Cluckers, Raf Loeser, François Nguyen, Kien Huu Vermeulen, Floris |
| contents | This work brings Mellin transforms into the realm of motivic integration. The new, larger class of motivic functions is stable under motivic Mellin and Fourier transforms, with general Fubini results and change of variables formulas. It specializes to $p$-adic integrals and $p$-adic Mellin transforms uniformly in $p$, with transfer principles between zero and positive characteristic local fields. In particular, it generalizes previous set-ups of motivic integration with Fubini from among others [16, 17, 18, 29, 9] and simplifies some aspects on the way by using the ideas of [10]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_17764 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Motivic Mellin transforms Cluckers, Raf Loeser, François Nguyen, Kien Huu Vermeulen, Floris Algebraic Geometry Logic Number Theory This work brings Mellin transforms into the realm of motivic integration. The new, larger class of motivic functions is stable under motivic Mellin and Fourier transforms, with general Fubini results and change of variables formulas. It specializes to $p$-adic integrals and $p$-adic Mellin transforms uniformly in $p$, with transfer principles between zero and positive characteristic local fields. In particular, it generalizes previous set-ups of motivic integration with Fubini from among others [16, 17, 18, 29, 9] and simplifies some aspects on the way by using the ideas of [10]. |
| title | Motivic Mellin transforms |
| topic | Algebraic Geometry Logic Number Theory |
| url | https://arxiv.org/abs/2412.17764 |