Fay Identities of Pfaffian Type for Hyperelliptic Curves Article Swipe

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YOU? · · 2023 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2312.12229

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.

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Pfaffian Hyperelliptic curve Mathematics Type (biology) Hyperelliptic curve cryptography Pure mathematics Matrix (chemical analysis) Theta function Algebra over a field Ecology Materials science Composite material Encryption Operating system Public-key cryptography Biology Elliptic curve cryptography Computer science

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Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2312.12229
PDF: https://arxiv.org/pdf/2312.12229
OA Status: green
References: 31
Related Works: 10
OpenAlex ID: https://openalex.org/W4390048901

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DOI: https://doi.org/10.48550/arxiv.2312.12229

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Title: Fay Identities of Pfaffian Type for Hyperelliptic Curves

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Type: preprint

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Language: en

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Publication year: 2023

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Publication date: 2023-12-19

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Authors: Gaëtan Borot, Thomas Buc-d’Alché

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Concepts: Pfaffian, Hyperelliptic curve, Mathematics, Type (biology), Hyperelliptic curve cryptography, Pure mathematics, Matrix (chemical analysis), Theta function, Algebra over a field, Ecology, Materials science, Composite material, Encryption, Operating system, Public-key cryptography, Biology, Elliptic curve cryptography, Computer science

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