arXiv subjects

Sandra Marcello

Publications and source records attributed to Sandra Marcello.

4 recordsLinked to original sources

arXiv2011

Operand Folding Hardware Multipliers

This paper describes a new accumulate-and-add multiplication algorithm. The method partitions one of the operands and re-combines the results of computations done with each of the partitions. The resulting design turns-out to be both compact and fast. When the operands' bit-length $m$ is 1024, the new algorithm requires only $0.194m+56$ additions (on average), this is about half the number of additions required by the classical accumulate-and-add multiplication algorithm ($\frac{m}2$).

cs.MS↗

arXiv2004

Géométrie, points rationnels et itérés des automorphismes de l'espace affine

We study over a number field, the iterates of automorphisms of the affine space. More precisely, we are interested in the periodic and non-periodic points; for the former the questions are similar to the ones about torsion points on abelian varieties, for the latter the questions are similar to the problems on counting rational points on varieties. In order to study this problem, we define geometric invariants, which are defined thanks to the cone of divisors associated to some varieties constructed from the automorphisms. We study, in all dimension, these invariants and bound them above for one of them we obtain a bound depending on the dynamical degree, this bound is reach by some automorphisms, in particular this bound is optimal. For an other invariant, we obtain in all dimension, thanks to a geometrical construction and under some geometric conditions, a better bound.

math.NT↗

arXiv2003

Sur la dynamique p-adique arithmétique des automorphismes de l'espace affine

We show that the set of periods of an automorphism of the affine plane defined over a $p$-adic field is bounded above by a constant independent from the automorphism. We deduce from this result a new proof in arithmetic dynamics of the Silverman's conjecture in dimension 2.

math.NT↗

arXiv2003

Sur des invariants géométriques associés aux automorphismes du plan affine

We associate to each automorphism of the plane, a geometric construction with some properties, it is the {\it{canonical resolution}}. We study the geometry of the canonical resolution, we deduce from it an upper bound for a geometric invariant (the ample index) linked to an automorphism of the affine plane and we link the structure of the effective cone of the surface we get to values of another geometric invariant (the effective index).

math.AG↗