On hyperelliptic abelian functions of genus 3

The affine ring AA of the affine Jacobian variety J(X)∖ΘJ(X)∖Θ of a hyperelliptic curve of genus 33 is studied as a DD module. A conjecture on the minimal DD-free resolution previously proposed is proved in this case. As a by-product a linear basis of AA is explicitly constructed in terms of derivatives of Klein’s hyperelliptic ℘℘-functions.