5 papers
Fast evaluation of Riemann theta functions in any dimension
Noam D. Elkies, Jean Kieffer
We describe an algorithm to numerically evaluate Riemann theta functions in any dimension in quasi-linear time in terms of the required precision, uniformly on reduced input. This…
The asymptotic distribution of Elkies primes for reductions of abelian varieties is Gaussian
Alexandre Benoist, Jean Kieffer
We generalize the notion of Elkies primes for elliptic curves to the setting of abelian varieties with real multiplication (RM), and prove the following. Let be an abelian vari…
Evaluating modular equations for abelian surfaces
Jean Kieffer
We design efficient algorithms to evaluate modular equations of Siegel and Hilbert type for abelian surfaces over number fields or finite fields using complex approximations. Their…
Computing isogenies from modular equations in genus two
Jean Kieffer, Aurel Page, Damien Robert
We present an algorithm solving the following problem: given two genus 2 curves over a field k with isogenous Jacobians, compute such an isogeny explicitly. This isogeny can be eit…
Spanning isogeny classes of principally polarized abelian surfaces with RM
Jean Kieffer
We describe how isogenies between principally polarized abelian surfaces (PPAS) with real multiplication (RM) can be decomposed into elementary isogeny types. This leads to a strat…