Voici la liste complète (par ordre chronologique inverse) des rapports de
recherche du laboratoire parus en 1998, avec leurs
résumés. Lorsque le titre d'un rapport apparaît souligné, il
est possible d'en charger une version postscript ou DVI en cliquant dessus. Pour recevoir
un rapport en version papier, contactez son auteur ou envoyez un
message électronique à :
Pierre.Ageron@math.unicaen.fr
1998-28 V. MAUDUIT,
Euler pseudoprime polynomials, strong pseudoprime polynomials
and Belekamp's algorithm
We introduce a particular rank one Drinfeld module to get an exponentiation for
polynomials. We interpret Berlekamp's algorithm in these terms.
1998-27 S. LOUBOUTIN,
Computation of L(0,chi) and of relative class numbers of CM-fields
We develop an efficient technique for computing the exact value at s=0 of abelian Hecke
L-functions over totally real number fields.
1998-26 S. LOUBOUTIN,
Hasse unit indices of dihedral octic CM-fields
We develop a technique for computing Hasse unit indices of dihedral octic CM-fields,
stemming from a simple test whether an element is a square.
We prove that the lattices of some counterexamples to the congruence lattice problem
cannot have permutable
congruences. We also isolate finite analogues of these results, as
amalgamation properties.
1998-24 P. AGERON, Note sur les LD-monoïdes réflexifs
Nous identifions les demi-treillis de Heyting aux LD-monoïdes
commutatifs satisfaisant deux équations simples.
We describe a simple algorithm for computing Kashiwara's global crystal basis
of a finite-dimensional irreductible representation of U_q(sl_n).
1998-18 G. GRATZER and F. WEHRUNG,
Flat semilattices
1998-16 N. CREIGNOU, Complexity versus stability for classes of
propositional formulas
1998-15 D. ESSOUABRI, Preuve d'une conjecture de Hardy et Littewood (via
la généralisation d'un résultat de Mahler)
On généralise un théorème d'existence de prolongement
méromorphe au plan complexe de certaines séries, dû à Mahler.
Comme application, nous obtenons une démonstration d'une conjecture de
Hardy et Littewood concernant l'existence et les propriétés du
prolongement
méromorphe de séries de Dirichlet.
1998-14 A. DURAND, C. LAUTEMAN and M. MORE, Counting results in weak
formalisms
We present a coding device based on a collision-free hashing technique,
leading to a completely elementary proof for the polylog counting capability of
first-order logic (with built-in arithmetic), AC0-circuits, rudimentary arithmetic, the
Linear Hierarchy and monadic-second order logic with addition.
1998-13 P. DEHORNOY, On completeness of word reversing
Word reversing is a combinatorial operation on words that detects pairs of equivalent
words in monoids that admit a presentation of a certain form. Here we give a condition
for this method to be complete in the sense that every pair of equivalent words can be
detected by word reversing. As an application, we show that the Artin groups of
Coxeter type B are left orderable.
We give a combinatorial algorithm for computing Zelevinsky's involution
of the set of isomorphism classes of irreducible representations of the affine Hecke
algebra
H^m(t) when t is a primitive nth root of 1. We show that the same map can also be
interpreted in terms of aperiodic nilpotent orbits of Z/nZ-graded
vector spaces.
1998-11 S. LEIDWANGER,
Basic representations of type A affine Lie algebras and the combinatorics
of partitions
The purpose of this paper is to show that the bijection between partitions
and their cores and quotients can be understoood as a combinatorial image of
the transition from the principal to the homogeneous picture
in the realm of affine Lie algebras.
1998-10 A. B. SOSSINSKY,
Smooth manifolds with singularities and classical mechanics
A new generalization of the notion of smooth manifold, which allows the generalized
manifold to have singularities, is presented and illustrated by the study of certain
objects from elementary classical mechanics, namely nongeneric plane hinge mechanisms.
The infinite braid
group admits a left self-distributive structure. In particular,
it includes a free monogenerated left self-distributive system, and,
therefore, it inherits the properties of the latter algebraic object.
Here we discuss how such properties translate into the language of
braids. We state new results about braids and propose a list of open
questions.
1998-8 J. NGATCHOU WANDJI and N. LAIB,
Limiting distributions of weighted processes of residuals. Application to
testing time series
We present new methods for testing the goodness-of-fit of linear or nonlinear
regression or autoregression functions for parametric models of order 1, under
stationarity and ergodicity assumptions. Our basic procedure is based on a measure of
the deviation between a weighted process of residuals and a parametric estimator of the
cumulated conditional mean function.
We study notions such as finite presentability and coherence, for partially ordered
abelian groups and vector spaces. We obtain characterization and representation
results. Futher, we establish connections with interpolations.
We extend and study the usual definition of coherence, for modules over rings, to
partially ordered right modules over a large class of partially ordered rings, called
normally ordered rings. In this situation, coherence is equivalent to saying that
solution sets of finite systems of inequalities are finitely generated semimodules.
Some identities due to Karlin and Szegö which provide a relationship between determinants
of classical orthogonal polynomials of Wronskian and Hankel type are shown to be specializations
of a general algebraic identity between minors of a matrix.
1998-4 Y. AUBRY, Principal imaginary bicyclic function fields
Let q be a power of an odd prime, k be the field Fq(x)
and K be a real quadratic extension of k. We show that there is no imaginary
quadratic extension L of K of such that L/k is Galois, with its Galois group isomorphic to the
Klein group and such that the ideal class
number of L is equal to 1.
1998-3 Y. AUBRY, Une formule de nombre de classes
Nous donnons une formule sur le nombre de classes d'idéaux d'une extension quadratique
imaginaire d'une extension quadratique réelle de Fq(x) en termes de sommes de caractères finies.
We study the relationships among existing results about representations of distributive
semilattices by ideals in dimension groups, von Neumann regular rings, C*-algebras and
complemented modular lattices. We prove additional representation results which exhibit further
connections with the scattered literature in these different topics.
Let A and B be lattices with zero. Their classical tensor product as join-semilattices with zero
is not, in general, a lattice. We define a very natural condition under which it is. Under the
same condition, we prove that the join-semilattice with zero of compact congruences on the
tensor product of A and B is isomorphic to the tensor product of the join-semilattices with zero
of compact congruences on A and on B.
