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| In this discussion a program for computing first terms of the series expansion for $\sigma$-function associated with a genus two curve is presented. The series is computed for the curve in its canonical form. $\sigma$-Functions associated with ... |
| ![enter image description here][1] ## Abstract ## On a given curve, we obtain division polynomials for 3- and 4-torsion divisors. We also find all 3- and 4-torsion divisors by means of (i) solving the Jacobi inversion problem, and (ii) solving the... |
| ![Computation of n-torsion divisors on a genus 4 hyperelliptic curve][2] **ABSTRACT**: In this discussion 2-, 3-, and 4-torsion divisors are computed directly from points of the Jacobian variety of a genus 4 hyperelliptic curve in the canonical... |
| **ABSTRACT:** An efficient criteria to single out the characteristic of vector of Riemann constants on an algebraic curve is suggested. It perfectly works on non-hyperelliptic and hyperelliptic curves, and allows to select the unique characteristic... |
| ![Uniformization of a genus 3 trigonal curve][1] **ABSTRACT (original article)**: Numerical tools for computation of ℘-functions, also known as Kleinian, or multiply periodic, are proposed. In this connection, computation of periods of the both... |
| The Jacobi inversion problem can be used to accomplish **addition on a curve**. As mentioned in the beginning of this discussion, a divisor $D$ can be of arbitrary degree $N\geqslant g$. Then we compute $\mathcal{A}(D)$ point by point, and... |