Eilbeck, J. C.; Enolski, V. Z.; Matsutani, S.; Ônishi, Yoshihiro; Previato, E. Abelian functions for trigonal curves of genus three. (English) Zbl 1210.14032 Int. Math. Res. Not. 2008, Article ID rnm140, 38 p. (2008). Summary: We develop the theory of generalized Weierstrass \(\sigma\)- and \(\wp\)-functions defined on a general trigonal curve of genus three. In particular, we give a list of the associated partial differential equations satisfied by the \(\wp\)-functions, a proof that the coefficients of the power series expansion of the \(\sigma\)-function are polynomials of coefficients of the defining equation of the curve, and the derivation of two addition formulae. Cited in 2 ReviewsCited in 36 Documents MSC: 14H42 Theta functions and curves; Schottky problem 14H45 Special algebraic curves and curves of low genus 33E05 Elliptic functions and integrals 37K20 Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions PDFBibTeX XMLCite \textit{J. C. Eilbeck} et al., Int. Math. Res. Not. 2008, Article ID rnm140, 38 p. (2008; Zbl 1210.14032) Full Text: DOI arXiv Link