Preprint 2023-06
Gaëtan Borot, Thomas Bus-d'Alché
Fay Identities of Pfaffian type for hyperelliptic Curves.
Abstract: 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 curves, and in this form we reprove them by direct geometric methods.
37 pp.
Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 2023-06