Geodesic
Fay Identities of Pfaffian Type for Hyperelliptic Curves
Symmetry, integrability and geometry: methods and applications, Tome 20 (2024) Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Keywords: random matrix theory, theta function, Fay's identity, hyperelliptic curves. 
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     author = {Ga\"etan Borot and Thomas Buc-D{\textquotedblright}Alche},
     title = {Fay {Identities} of {Pfaffian} {Type} for {Hyperelliptic} {Curves}},
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Gaëtan Borot; Thomas Buc-D”Alche. Fay Identities of Pfaffian Type for Hyperelliptic Curves. Symmetry, integrability and geometry: methods and applications, Tome 20 (2024). http://geodesic.mathdoc.fr/item/SIGMA_2024_20_a53/

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