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Computational Aspects of Jacobians of Hyperelliptic Curves

Publications associées (135)

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On the Reduction of Points on Abelian Varieties and Tori

Antonella Perucca

Let G be the product of an abelian variety and a torus defined over a number field K. Let R-1, ..., R-n be points in G(K). Let l be a rational prime, and let a(1), ..., a(n) be nonnegative integers. Consider the set of primes p of K satisfying the followin ...

2011

Sampling Curves with Finite Rate of Innovation

Thierry Blu, Hanjie Pan, Pier Luigi Dragotti

We focus on a specific class of curves that can be parametrized using a finite number of variables in two dimensions. The corresponding indicator plane, which is a binary image, has infinite bandwidth and can not be sampled and perfectly reconstructed with ...

2011

Sup-norms of Eigenfunctions on Arithmetic Ellipsoids

Philippe Michel

Let B be a positive quaternion algebra, and let O subset of B be an Eichler order. There is associated, in a natural way, a variety X = X(O) the connected components of which are indexed by the ideal classes of O and are isomorphic to spheres. This variety ...

Oxford University Press2011

Equidistribution of Heegner points and ternary quadratic forms

Dimitar Petkov Jetchev

We prove new equidistribution results for Galois orbits of Heegner points with respect to single reduction maps at inert primes. The arguments are based on two different techniques: primitive representations of integers by quadratic forms and distribution ...

Springer Verlag2011

Distribution of periodic torus orbits and Duke's theorem for cubic fields

Philippe Michel

We study periodic torus orbits on spaces of lattices. Using the action of the group of adelic points of the underlying tori, we define a natural equivalence relation on these orbits, and show that the equivalence classes become uniformly distributed. This ...

2011

Efficient and side-channel-aware implementations of elliptic curve cryptosystems over prime fields

Yusuf Leblebici

Elliptic curve cryptosystems (ECCs) are utilised as an alternative to traditional public-key cryptosystems, and are more suitable for resource-limited environments because of smaller parameter size. In this study, the authors carry out a thorough investiga ...

2010

A counterexample to the local-global principle of linear dependence for Abelian varieties

Antonella Perucca, Peter Simon Jossen

Let A be an Abelian variety defined over a number field k. Let P be a point in A(k) and let X be a subgroup of A(k). Gajda and Kowalski asked in 2002 whether it is true that the point P belongs to X if and only if the point (P mod p) belongs to (X mod p) f ...

2010

Sur la méthode de Buser-Silhol pour l'uniformisation des surfaces de Riemann hyperelliptiques

Grégoire Aubry

The Uniformization Theorem due to Koebe and Poincaré implies that every compact Riemann surface of genus greater or equal to 2 can be endowed with a metric of constant curvature – 1. On the other hand, a compact Riemann surface is a complex algebraic curve ...

EPFL2010

Arithmetic Bounds-Lenstra's Constant and Torsion of K-Groups

Julien Houriet

This thesis is concerned with computations of bounds for two different arithmetic invariants. In both cases it is done with the intention of proving some algebraic or arithmetic properties for number fields. The first part is devoted to computations of low ...

EPFL2010

Diagonal Quartic Surfaces And Transcendental Elements Of The Brauer Group

Evis Ieronymou

We exhibit central simple algebras over the function field of a diagonal quartic surface over the complex numbers that represent the 2-torsion part of its Brauer group. We investigate whether the 2-primary part of the Brauer group of a diagonal quartic sur ...

Cambridge University Press2010