S-Units Attached to Genus 3 Hyperelliptic Curves Original Research Article

LetCbe a hyperelliptic curve of genus 3, with potentially good reduction at all primes not dividing 3, defined over a number fieldK. A function defined on the JacobianJofCwill be constructed which, when evaluated at the 3-torsion pointsJ[3] ofJ, will giveS-units inK(J[3]); at most, the setSwill consist of primes dividing 3.