Sur la monogeneite de l'anneau des entiers de certains corps de rayon

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Sur la monogénéité de l'anneau des entiers d'une extension diédrale imaginaire de degré 2p (p premier)

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Extensions cycliques cubiques monogènes de l'anneau des entiers d'un corps quadratique

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Extensions cycliques cubiques monogènes de l'anneau des entiers d'un corps quadratique imaginaire

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Opérateurs linéaires continus d'extension dans des intersections de classes ultradifférentiables

Mityagin proved that the Tchebyshev polynomials form a Schauder basis of the space of C^∞ functions on the interval [?1,1]. Thus, he deduced an explicit continuous linear extension operator. These results were extended, by Goncharov, to compact sets which do not satisfy the Markov's inequalities. On the other hand, Tidten gave examples of compact sets for which there is no continuous linear extension operator. In this Note, we generalize these works to ultradifferentiable classes of functions built on the model of the intersection of non quasi-analytic Gevrey classes. We get, among other things, a Whitney linear extension theorem for ultradifferentiable jets of Beurling type. To cite this article: P. Beaugendre, C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

Modèles entiers des courbes hyperelliptiques sur un corps de valuation discrète

Let be a hyperelliptic curve of genus over a discrete valuation field . In this article we study the models of over the ring of integers of . To each Weierstrass model (that is a projective model arising from a hyperelliptic equation of with integral coefficients), one can associate a (valuation of) discriminant. Then we give a criterion for a Weierstrass model to have minimal discriminant. We show also that in the most cases, the minimal regular model of over dominates every minimal Weierstrass model. Some classical facts concerning Weierstrass models over of elliptic curves are generalized to hyperelliptic curves, and some others are proved in this new setting.

     

Interprétation bijective d'une récurrence des nombres de Motzkin

The purpose of this note is to give a combinatorial proof of the three-term linear recurrence for Motzkin numbers. The present work is inspired by Rémy's combinatorial proof of the linear recurrence for Catalan numbers (RAIRO Inform. Theor. 19(2) (1985) 179) and the more recent proof given by Foata and Zeilberger (J. Combin. Theory Ser. A 80(2) (1997) 380) for Schröder numbers (Z. Math. Phys. 15 (1870) 361).     

Valeurs d'une fonction de Picard en des points algébriques

Using geometric tools introduced by P. Cohen, H. Shiga, J. Wolfart and G. Wüstholz, we show in Theorem 1 that when a certain Gauss hypergeometric function takes an algebraic value at an algebraic point, then another Gauss hypergeometric function takes a transcendental value at a related algebraic point. Using Appell hypergeometric functions, which generalize to two variables the Gauss functions, we study values at algebraic points of a new transcendental function defined in terms of these two functions. By Theorem 2, these values correspond to abelian varieties in the same isogeny class. Using a result of Edixhoven-Yafaev [B. Edixhoven, A. Yafaev, Subvarieties of Shimura varieties, Ann. of Math. 157 (2003) 621-645], this last result is in turn related to the distribution of the moduli of such abelian varieties in certain Shimura varieties.     

Une remarque sur l'orthogonalité de l'image au noyau d'une dérivation généralisée

In this paper we introduce the notion of the pair of operators having the Fuglede-Putnam property in a two-sided ideal of . The characterization of this class allows us to generalize the recent result of F. Kittaneh. We also give some applications of this result.

     

Comportement des noyaux de la chaleur des opérateurs de Schrödinger et applications à certaines équations paraboliques semi-linéaires

We consider general Schrödinger operators on domains of Riemannian manifolds with possibly exponential volume growth. We prove sharp large time Gaussian upper bounds. These bounds are then used to prove new Lp-Lp estimates for the corresponding semigroups. Applications to semi-linear parabolic equations are given.     

Interprétation combinatoire des moments négatifs des valeurs de fonctions L au bord de la bande critique

We give a combinatorial interpretation of the negative moments of the values at the edge of the critical strip of the L functions of modular forms of GL(2) and GL(3). We deduce some results about the size of these numbers.     

Opérateurs d'extension linéaires explicites dans des intersections de classes ultradifférentiables

B. S. Mityagin proved that the Chebyshev polynomials form a Schauder basis of the space of C ^∞ functions on the interval [–1,1]. Whereof he deduced an explicit continuous linear extension operator. These results were extended, by A. Goncharov, to compact sets without Markov's property. On the reverse, M. Tidten gave examples of compact sets for which there is no continuous linear extension operator. In this paper, we generalize these works to the intersections of ultradifferentiable classes of functions built on the model of the non quasianalytic intersection of Gevrey classes. We get, among other things, a Whitney linear extension theorem for ultradifferentiable jets of Beurling type.     

L'espace des sélections d'une dendrite

We prove that the selection space of a nondegenerate dendrite is homeomorphic to ?².     

Extension du domaine de définition d'une série de Dirichlet multiplicative

We prove a general theorem which allows to approach a multiplicative Dirichlet series with two variables by a known series.     

Singularités topologiques des systoles généralisées

We prove that a generalized systole defined by functions with positive definite Hessians is a topological Morse function such that critical points are eutactic points. We deduce that systole is a topological Morse function on Teichmüller space.     

Sur la répartition des entiers premiers à un entier sans petit facteur premier

Let Mk(q;h) be the kth moment of the number of integers coprime to q in an interval of length h centered on its mean . By comparison with the kth centered moment of the binomial distribution with parameters h and P, for which we show

μk(h,P)?(ck)^k/2(k+hP(1−P)⁾k/2,