Abelian functions associated with a cyclic tetragonal curve of genus six

M. England, J. C. Eilbeck

Research output: Contribution to journalArticlepeer-review

17 Citations (Scopus)


We develop the theory of Abelian functions defined using a tetragonal curve of genus six, discussing in detail the cyclic curve y4 = x 5 + ?4x4 + ?3x 3 + ?2x2 + ?1x + ?0. We construct Abelian functions using the multivariate s-function associated with the curve, generalizing 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 s(u) and a new addition formula. © 2009 IOP Publishing Ltd.

Original languageEnglish
Article number095210
JournalJournal of Physics A: Mathematical and Theoretical
Issue number9
Publication statusPublished - 2009


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