Adding Divisors on hyperelliptic curves via interpolation polynomials

Julia Bernatska, Yaacov Kopeliovich, Tony Shaska

Published 2019-12-31Version 1

An effective procedure to reduce any non-special divisor to an equivalent divisor composed of the number of points equal to the genus of a curve is suggested. The hyperelliptic case is considered as the simplest model. The advantage of the proposed procedure is its explicitness: all steps are realized through arithmetic operations on polynomials. The resulting reduced divisor is obtained in the form of Jacobi inversion problem which unambiguously defines the divisor, at the same time values of Abelian functions on the divisor are obtained.