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European Journal of Mathematics

, Volume 5, Issue 3, pp 712–719 | Cite as

On the problem of differentiation of hyperelliptic functions

  • Elena Yu. BunkovaEmail author
Research Article
  • 6 Downloads

Abstract

We describe a construction that leads to an explicit solution of the problem of differentiation of hyperelliptic functions. A classical genus \(g=1\) example of such a solution is the result of Frobenius and Stickelberger (J Reine Angew Math 92:311–337, 1882). Our method follows the works Buchstaber (Proc Steklov Inst Math 294:176–200, 2016) and Bunkova (Eur J Math 4(1):93–112, 2018) that led to constructions of explicit solutions of the problem for genus \(g=2\) and \(g=3\).

Keywords

Abelian functions Elliptic functions Jacobians Hyperelliptic curves Hyperelliptic functions Lie algebra of derivations Polynomial vector fields 

Mathematics Subject Classification

14H52 32N99 33E05 58J26 

Notes

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Steklov Mathematical Institute of Russian Academy of SciencesMoscowRussia

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