ar X iv : 0 80 6 . 23 77 v 2 [ m at h . A G ] 3 N ov 2 00 8 Abelian functions associated with a cyclic tetragonal curve of genus six
نویسندگان
چکیده
We develop the theory of Abelian functions defined using a tetragonal curve of genus six, discussing in detail the cyclic curve y 4 = x 5 + λ 4 x 4 + λ 3 x 3 + λ 2 x 2 + λ 1 x + λ 0. We construct Abelian functions using the multivariate σ-function associated to the curve, generalising the theory of the Weierstrass ℘-function. We demonstrate that such functions can give a solution to the KP-equation, outlining how a general class of solutions could be generated using a wider class of curves. We also present the associated partial differential equations satisfied by the functions, the solution of the Jacobi Inversion Problem, a power series expansion for σ(u) and a new addition formula.
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