6533b82bfe1ef96bd128e2ae
RESEARCH PRODUCT
The periods of the generalized Jacobian of a complex elliptic curve
Alfonso Di BartoloGiovanni Falconesubject
Elliptic curve point multiplicationQuarter periodGeneralized JacobianModular elliptic curveJacobian curveMathematical analysisHessian form of an elliptic curveGeometry and TopologyGeneralized Jacobians toroidal Lie groupsSettore MAT/03 - GeometriaTripling-oriented Doche–Icart–Kohel curveMathematicsJacobi elliptic functionsdescription
Abstract We show that the toroidal Lie group G = ℂ2/Λ, where Λ is the lattice generated by (1, 0), (0, 1) and (τ̂, τ͂), with τ̂ ∉ ℝ, is isomorphic to the generalized Jacobian JL of the complex elliptic curve C with modulus τ̂, defined by any divisor class L ≡ (M) + (N) of C fulfilling M − N = [℘ (τ͂) : ℘´(τ͂) : 1] ∈ C. This follows from an apparently new relation between the Weierstrass sigma and elliptic functions.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2015-01-01 |