Generalised elliptic functions

@article{England2011GeneralisedEF,
  title={Generalised elliptic functions},
  author={Matthew England and C. Athorne},
  journal={Central European Journal of Mathematics},
  year={2011},
  volume={10},
  pages={1655-1672}
}
  • Matthew England, C. Athorne
  • Published 2011
  • Mathematics, Physics
  • Central European Journal of Mathematics
  • We consider multiply periodic functions, sometimes called Abelian functions, defined with respect to the period matrices associated with classes of algebraic curves. We realise them as generalisations of the Weierstraß ℘-function using two different approaches. These functions arise naturally as solutions to some of the important equations of mathematical physics and their differential equations, addition formulae, and applications have all been recent topics of study.The first approach… CONTINUE READING

    Tables from this paper

    References

    SHOWING 1-10 OF 40 REFERENCES
    Abelian functions associated with a cyclic tetragonal curve of genus six
    • 20
    • Highly Influential
    • PDF
    On higher genus Weierstrass sigma-function
    • 18
    • PDF
    Deriving Bases for Abelian Functions Matthew England
    • 4
    • PDF
    Abelian Functions: Abel's Theorem and the Allied Theory of Theta Functions
    • 136
    • PDF
    Genus 4 trigonal reduction of the Benney equations
    • 27
    • PDF
    Hyperelliptic reduction of the Benney moment equations
    • 20
    • PDF
    Abelian functions for cyclic trigonal curves of genus 4
    • 36
    • PDF
    Abelian functions associated with genus three algebraic curves
    • 13
    • Highly Influential
    • PDF