Abelian functions associated with a cyclic tetragonal curve of genus six

الأصل · EN

We develop the theory of Abelian functions defined using a tetragonal curve of genus six, discussing in detail the cyclic curve y⁴ = x⁵ + λ₄x⁴ + λ₃x³ + λ₂x² + λ₁x + λ₀. 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() and a new addition formula.