Solution of the Jacobi inversion problem on non-hyperelliptic curves. (English) Zbl 1526.30053
Summary: In this paper, we propose a method of solving the Jacobi inversion problem in terms of multiply periodic \(\wp\) functions, also called Kleinian \(\wp\) functions. This result is based on the recently developed theory of multivariable sigma functions for \((n, s)\)-curves. Considering \((n, s)\)-curves as canonical representatives in the corresponding classes of bi-rationally equivalent plane algebraic curves, we claim that the Jacobi inversion problem on plane algebraic curves is solved completely. Explicit solutions on trigonal, tetragonal and pentagonal curves are given as an illustration.
MSC:
| 30F10 | Compact Riemann surfaces and uniformization |
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