Add to ORKGWe design algorithms to efficiently evaluate genus 2 modular polyno-mials of Siegel and Hilbert type over number fields, using complex approximations. Under heuristics related to the computation of theta functions in quasi-linear time, the output is provably correct. Our algorithms also apply to finite fields via lifting
International audienceSchoof's classic algorithm allows point-counting for elliptic curves over fini...
Let k be a field of large enough characteristic. We present an algorithm solving the following probl...
This thesis is about arithmetic, analytic and algorithmic aspects of modular curves and modular form...
Substantial rewrite. The main complexity result is improved. An important heuristic assumption is pr...
We propose to generalize the work of Régis Dupont for computing modular polynomials in dimension 2 t...
AbstractWe give a new method for generating genus 2 curves over a finite field with a given number o...
Let A/Fq be an ordinary abelian surface. We explain how to use the Siegel modular polynomials, and i...
To appear in Mathematics of Computation.We analyse and compare the complexity of several algorithms ...
Modular forms are tremendously important in various areas of mathematics, from number theory and alg...
International audienceWe outline an algorithm to compute θ(z, τ) in genus 2 in quasi-optimal time, b...
My thesis looks at ordinary abelian varieties defined with maximal real multiplication. I define mod...
Les polynômes modulaires sont utilisés dans le calcul de graphes d’isogénies, le calcul des polynôme...
Let k be a field of even characteristic and M2(k) the moduli space of the genus 2 curves defined ove...
Let E be an elliptic curve over a field K and L a prime.There exists an elliptic curve E* related to...
International audienceSchoof's classic algorithm allows point-counting for elliptic curves over fini...
Let k be a field of large enough characteristic. We present an algorithm solving the following probl...
This thesis is about arithmetic, analytic and algorithmic aspects of modular curves and modular form...
Substantial rewrite. The main complexity result is improved. An important heuristic assumption is pr...
We propose to generalize the work of Régis Dupont for computing modular polynomials in dimension 2 t...
AbstractWe give a new method for generating genus 2 curves over a finite field with a given number o...
Let A/Fq be an ordinary abelian surface. We explain how to use the Siegel modular polynomials, and i...
To appear in Mathematics of Computation.We analyse and compare the complexity of several algorithms ...
Modular forms are tremendously important in various areas of mathematics, from number theory and alg...
International audienceWe outline an algorithm to compute θ(z, τ) in genus 2 in quasi-optimal time, b...
My thesis looks at ordinary abelian varieties defined with maximal real multiplication. I define mod...
Les polynômes modulaires sont utilisés dans le calcul de graphes d’isogénies, le calcul des polynôme...
Let k be a field of even characteristic and M2(k) the moduli space of the genus 2 curves defined ove...
Let E be an elliptic curve over a field K and L a prime.There exists an elliptic curve E* related to...
International audienceSchoof's classic algorithm allows point-counting for elliptic curves over fini...
Let k be a field of large enough characteristic. We present an algorithm solving the following probl...
This thesis is about arithmetic, analytic and algorithmic aspects of modular curves and modular form...