European Journal of Mathematics

, Volume 4, Issue 1, pp 93–112 | Cite as

Differentiation of genus 3 hyperelliptic functions

  • Elena Yu. Bunkova
Research Article


We give an explicit solution to the problem of differentiation of hyperelliptic functions in genus 3 case. It is a genus 3 analogue of the result of Frobenius and Stickelberger (J Reine Angew Math 92:311–337, 1882). Our method is based on the series of works by Buchstaber, Enolskii and Leikin. First we introduce a polynomial map \(p:\mathbb {C}^{3g} \rightarrow \mathbb {C}^{2g}\) . Next for \(g = 1,2,3\) we provide 3g polynomial vector fields in \(\mathbb {C}^{3g}\) projectable for p and describe their polynomial Lie algebras. Finally we obtain the corresponding derivations of the field of hyperelliptic functions.


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

Mathematics Subject Classification

14H52 32N99 33E05 58J26 



The author thanks Victor M. Buchstaber for fruitful discussions of the results.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

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

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