Computing class polynomials for abelian surfaces
A Enge, E Thomé - Experimental Mathematics, 2014 - Taylor & Francis
A Enge, E Thomé
Experimental Mathematics, 2014•Taylor & FrancisWe describe a quasilinear algorithm for computing Igusa class polynomials of Jacobians of
genus-2 curves via complex floating-point approximations of their roots. After providing an
explicit treatment of the computations in quartic CM fields and their Galois closures, we
pursue an approach due to Dupont for evaluating ϑ-constants in quasilinear time using
Newton iterations on the Borchardt mean. We report on experiments with our
implementation and present an example with class number 20 016.
genus-2 curves via complex floating-point approximations of their roots. After providing an
explicit treatment of the computations in quartic CM fields and their Galois closures, we
pursue an approach due to Dupont for evaluating ϑ-constants in quasilinear time using
Newton iterations on the Borchardt mean. We report on experiments with our
implementation and present an example with class number 20 016.
We describe a quasilinear algorithm for computing Igusa class polynomials of Jacobians of genus-2 curves via complex floating-point approximations of their roots. After providing an explicit treatment of the computations in quartic CM fields and their Galois closures, we pursue an approach due to Dupont for evaluating ϑ-constants in quasilinear time using Newton iterations on the Borchardt mean. We report on experiments with our implementation and present an example with class number 20 016.
Taylor & Francis Online以上显示的是最相近的搜索结果。 查看全部搜索结果