On the problem of differentiation of hyperelliptic functions

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 $$g=3$$ .