Abelian functions for cyclic trigonal curves of genus 4

S. Baldwin, J. C. Eilbeck, J. Gibbons, Y. Ônishi

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35 Citations (Scopus)


We discuss the theory of generalized Weierstrass s and P-functions defined on a trigonal curve of genus 4, following earlier work on the genus 3 case. The specific example of the "purely trigonal" (or "cyclic trigonal") curve y3 = x5 + ?4 x4 + ?3 x3 + ?2 x2 + ?1 x + ?0 is discussed in detail, including a list of some of the associated partial differential equations satisfied by the P-functions, and the derivation of addition formulae. © 2008 Elsevier Ltd. All rights reserved.

Original languageEnglish
Pages (from-to)450-467
Number of pages18
JournalJournal of Geometry and Physics
Issue number4
Publication statusPublished - Apr 2008


  • Abelian functions
  • Algebraic geometry
  • Cyclic trigonal curve
  • Kleinian sigma functions


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