\(S\)-units attached to genus 3 hyperelliptic curves (Q677618)

It is well-known that evaluating suitable functions on torsion points of elliptic curves over number fields yield units and those elliptic units are very useful in arithmetic. Some efforts have been made to extend this to higher genus curves, for instance, \textit{D. Grant} [Compos. Math. 94, No. 3, 311-320 (1994; Zbl 0828.11033)], treated the case of genus two and 3- and 4-torsion. The author works with genus 3 hyperelliptic curves and 3-torsion, producing algebraic integers which are units away from 3.