6 papers
Algebraic solution of the Jacobi inverse problem and explicit addition laws
Yaacov Kopeliovich
We formulate a solution to the Algebraic version of the Inverse Jacobi problem. Using this solution we produce explicit addition laws on any algebraic curve generalizing the law su…
Addition of Divisors on Hyperelliptic Curves via Interpolation Polynomials
Julia Bernatska, Yaacov Kopeliovich
Two problems are addressed: reduction of an arbitrary degree non-special divisor to the equivalent divisor of the degree equal to genus of a curve, and addition of divisors of arbi…
The addition on Jacobian varieties from a geometric viewpoint
Yaacov Kopeliovich, Tony Shaska
We give a geometric interpretation of the group law for Jacobian varieties by extending the geometric construction of chords and tangents on an elliptic curve. For any given algebr…
Thomae's Derivative Formulae for Trigonal Curves
Victor Enolski, Yaacov Kopeliovich, Shaul Zemel
In this paper we prove a Thomae derivative formula for trigonal curves admitting a non-singular affine model. This formula relates the derivatives of theta functions with rational…
Modular equations of order and Theta functions
Yaacov Kopeliovich
An algorithm to obtain equations between theta functions with integral characteristics evaluated at and for is presented.
Theta constants identities for Jacobians of cyclic 3-sheeted covers of the sphere and representations of the symmetric group
Yaacov Kopeliovich
We find identities between theta constants with rational characteristics evaluated at period matrix of a cyclic 3 sheeted cover of the sphere with branch points $λ_1...λ_…