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math-ph2022★ 3 cited
Solution of the Jacobi inversion problem on non-hyperelliptic curves
Julia Bernatska, Dmitry Leykin
In this paper we propose a method of solving the Jacobi inversion problem in terms of multiply periodic functions, also called Kleinian functions. This result is based…
math-ph2015★ 4 cited
On degenerate sigma-functions of genus two
Julia Bernatska, Dmitry Leykin
We obtain explicit expressions for genus 2 degenerate sigma-function in terms of genus sigma-function and elementary functions as solutions of a system of linear PDEs satisfied…
math-ph2013
Harmonic analysis on Lagrangian manifolds of integrable Hamiltonian systems
Julia Bernatska, Petro Holod
For an integrable Hamiltonian system we construct a representation of the phase space symmetry algebra over the space of functions on a Lagrangian manifold. The representation is a…