Determinant Formulae in Abelian Functions for a General Trigonal Curve of Degree Five

@article{nishi2012DeterminantFI,
  title={Determinant Formulae in Abelian Functions for a General Trigonal Curve of Degree Five},
  author={Y. {\^O}nishi},
  journal={Computational Methods and Function Theory},
  year={2012},
  volume={11},
  pages={547-574}
}
  • Y. Ônishi
  • Published 2012
  • Mathematics
  • Computational Methods and Function Theory
This paper gives a natural generalization of the Frobenius-Stickelberger formula and the Kiepert formula for elliptic functions [4, 5] to the curve of genus four defined by $$\matrix{^3+ (\mu_2x + \mu_5)y^2 + (\mu_4x^2 + \mu_7x + \mu_{10})y\cr \ \ \ \ \ \ \ \ \ \ \ \ }$$ (μj are constants). 
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We give the Frobenius–Stickelberger-type and Kiepert-type determinantal formulae for purely trigonal curves of genus three. We explain also general theory of Abelian functions for any trigonal curvesExpand
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Abstract In this paper we give an elegant generalization of the formula of Frobenius–Stickelberger from elliptic curve theory to all hyperelliptic curves. A formula of Kiepert type is also obtainedExpand
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