Recursion relation of hyperelliptic PSI-functions of genus two

DOI10.1080/10652460310001600609zbMath1041.11047arXivmath-ph/0105031OpenAlexW2040443053MaRDI QIDQ4454053

Shigeki Matsutani

Publication date: 7 March 2004

Published in: Integral Transforms and Special Functions (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0105031

zbMATH Keywords

hyperelliptic functionpsi-function

Mathematics Subject Classification ID

Special algebraic curves and curves of low genus (14H45) [https://zbmath.org/classification/?q=cc:11G30 Curves of arbitrary genus or genus ( e 1) over global fields (11G30)]

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A generalized Kiepert formula for \(C_{ab}\) curves ⋮ Sigma function solution of the initial value problem for Somos 5 sequences ⋮ Integrality and the Laurent phenomenon for Somos 4 and Somos 5 sequences ⋮ Inversion of hyperelliptic integrals of arbitrary genus with application to particle motion in general relativity ⋮ Analytic solutions and integrability for bilinear recurrences of order six ⋮ Ultraelliptic integrals and two-dimensional sigma functions

Cites Work

• Complex multiplication formulae for hyperelliptic curves of genus three
• Elliptic and hyperelliptic solutions of discrete Painlevé I and its extensions to higher order difference equations
• Formal groups in genus two.
• On the analogue of the division polynomials for hyperelliptic curves.
• A Generalization of a Formula of Eisenstein
• Determinant expressions for abelian functions in genus two

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