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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.19285 |
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| _version_ | 1866912393160818688 |
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| author | Rüd, Thomas |
| author_facet | Rüd, Thomas |
| contents | To answer a question about the distribution of products of elliptic curves in isogeny classes of abelian surfaces defined over finite fields, we compute specific orbital integrals in the group $\mathrm{GSp}_4$. More precisely, we compute integrals over the orbits of elements in the subgroup $\mathrm{GL}_2\times_{\det} \mathrm{GL}_2$. As a first step towards a complete solution of the problem, this article contains explicit computations for arbitrary orbital integrals of spherical functions over this subgroup, and also compute orbital integrals over $\mathrm{GSp}_4$ in a large number of cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_19285 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A comparison problem for abelian surfaces and descent for symplectic orbital integrals Rüd, Thomas Number Theory To answer a question about the distribution of products of elliptic curves in isogeny classes of abelian surfaces defined over finite fields, we compute specific orbital integrals in the group $\mathrm{GSp}_4$. More precisely, we compute integrals over the orbits of elements in the subgroup $\mathrm{GL}_2\times_{\det} \mathrm{GL}_2$. As a first step towards a complete solution of the problem, this article contains explicit computations for arbitrary orbital integrals of spherical functions over this subgroup, and also compute orbital integrals over $\mathrm{GSp}_4$ in a large number of cases. |
| title | A comparison problem for abelian surfaces and descent for symplectic orbital integrals |
| topic | Number Theory |
| url | https://arxiv.org/abs/2505.19285 |