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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2312.12229 |
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| _version_ | 1866916298387095552 |
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| author | Borot, Gaëtan Buc-d'Alché, Thomas |
| author_facet | Borot, Gaëtan Buc-d'Alché, Thomas |
| contents | We establish identities of Pfaffian type for the theta function associated with twice or half the period matrix of a hyperelliptic curve. They are implied by the large size asymptotic analysis of exact Pfaffian identities for expectation values of ratios of characteristic polynomials in ensembles of orthogonal or quaternionic self-dual random matrices. We show that they amount to identities for the theta function with the period matrix of a hyperelliptic curve, and in this form we reprove them by direct geometric methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_12229 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Fay Identities of Pfaffian Type for Hyperelliptic Curves Borot, Gaëtan Buc-d'Alché, Thomas Mathematical Physics Algebraic Geometry Probability 60B20, 14H42 We establish identities of Pfaffian type for the theta function associated with twice or half the period matrix of a hyperelliptic curve. They are implied by the large size asymptotic analysis of exact Pfaffian identities for expectation values of ratios of characteristic polynomials in ensembles of orthogonal or quaternionic self-dual random matrices. We show that they amount to identities for the theta function with the period matrix of a hyperelliptic curve, and in this form we reprove them by direct geometric methods. |
| title | Fay Identities of Pfaffian Type for Hyperelliptic Curves |
| topic | Mathematical Physics Algebraic Geometry Probability 60B20, 14H42 |
| url | https://arxiv.org/abs/2312.12229 |