English

Differentiation of Genus $4$ Hyperelliptic Functions

Exactly Solvable and Integrable Systems 2019-12-25 v1 Algebraic Geometry Complex Variables

Abstract

In this work we give an explicit solution to the problem of differentiation of hyperelliptic functions in genus 44 case. It is a genus 44 analogue of the classical result of F. G. Frobenius and L. Stickelberger [F. G. Frobenius, L. Stickelberger, "Uber die Differentiation der elliptischen Functionen nach den Perioden und Invarianten", J. Reine Angew. Math., 92 (1882), 311-337] in the case of elliptic functions. An explicit solution in the genus 22 case was given in [V. M. Buchstaber, "Polynomial dynamical systems and Korteweg-de Vries equation", Proc. Steklov Inst. Math., 294 (2016), 176-200]. An explicit solution in the genus 33 case was given in [E. Yu. Bunkova, "Differentiation of genus 3 hyperelliptic functions", European Journal of Mathematics, 4:1 (2018), 93-112].

Keywords

Cite

@article{arxiv.1912.11379,
  title  = {Differentiation of Genus $4$ Hyperelliptic Functions},
  author = {V. M. Buchstaber and E. Yu. Bunkova},
  journal= {arXiv preprint arXiv:1912.11379},
  year   = {2019}
}

Comments

arXiv admin note: text overlap with arXiv:1911.08266

R2 v1 2026-06-23T12:55:46.418Z