9 citations · 29 across the 8 of their papers we have counts for
11 papers
Computing the cohomology of Shimura curves in quasi-linear time
Rayane Baït, Aurel Page
Computing spaces of modular and automorphic forms is an important problem in algorithmic number theory, with in particular Diophantine applications to generalised Fermat and other…
Vignéras orbifolds: isospectrality, regulators, and torsion homology
Alex Bartel, Aurel Page
We develop a new approach to the isospectrality of the orbifolds constructed by Vignéras. We give fine sufficient criteria for i-isospectrality in given degree i and for representa…
Computing groups of Hecke characters
Pascal Molin, Aurel Page
We describe algorithms to represent and compute groups of Hecke characters. We make use of an id{è}lic point of view and obtain the whole family of such characters, including trans…
Sorting and labelling integral ideals in a number field
John Cremona, Aurel Page, Andrew V. Sutherland
We define a scheme for labelling and ordering integral ideals of number fields, including prime ideals as a special case. The order we define depends only on the choice of a monic…
Norm relations and computational problems in number fields
Jean-François Biasse, Claus Fieker, Tommy Hofmann +1
For a finite group , we introduce a generalization of norm relations in the group algebra . We give necessary and sufficient criteria for the existence of such rel…
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…
Codes from unit groups of division algebras over number fields
Christian Maire, Aurel Page
Lenstra and Guruswami described number field analogues of the algebraic geometry codes of Goppa. Recently, the first author and Oggier generalised these constructions to other arit…
Group representations in the homology of 3-manifolds
Alex Bartel, Aurel Page
If M is a manifold with an action of a group G, then the homology group H_1(M,Q) is naturally a Q[G]-module, where Q[G] denotes the rational group ring. We prove that for every fin…
Torsion homology and regulators of isospectral manifolds
Alex Bartel, Aurel Page
Given a finite group G, a G-covering of closed Riemannian manifolds, and a so-called G-relation, a construction of Sunada produces a pair of manifolds M_1 and M_2 that are strongly…
An algorithm for the principal ideal problem in indefinite quaternion algebras
Aurel Page
Deciding whether an ideal of a number field is principal and finding a generator is a fundamental problem with many applications in computational number theory. For indefinite quat…
Computing arithmetic Kleinian groups
Aurel Page
Arithmetic Kleinian groups are arithmetic lattices in PSL_2(C). We present an algorithm which, given such a group Gamma, returns a fundamental domain and a finite presentation for…