2019/12/23 by Victor Matveevich Buchstaber, Buchstaber, V. M., E. Yu. Bunkova +1
Computer Science · Physics and Astronomy · #11G05 #14H45 #37K20 #Algebraic Geometry (math.AG) #Coding theory and cryptography #Complex Variables (math.CV) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Nonlinear Waves and Solitons #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1912.11379
openalex publication_date 2019/12/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this work we give an explicit solution to the problem of differentiation of hyperelliptic functions in genus 4 case. It is a genus 4 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 2 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 3 case was given in [E. Yu. Bunkova, "Differentiation of genus 3 hyperelliptic functions", European Journal of Mathematics, 4:1 (2018), 93-112].