5 citations · 13 across the 13 of their papers we have counts for
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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…
Sign choices in the AGM for genus two theta constants
Jean Kieffer
Existing algorithms to compute genus 2 theta constants in quasi-linear time use Borchardt sequences, an analogue of the arithmetic-geometric mean for four complex numbers. In this…
Degree and height estimates for modular equations on PEL Shimura varieties
Jean Kieffer
We define modular equations in the setting of PEL Shimura varieties as equations describing Hecke correspondences, and prove upper bounds on their degrees and heights. This extends…
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…