Sur une application de la formule de Selberg-Delange

F. Ben Saïd; J.-L. Nicolas

Displaying similar documents to “Sur une application de la formule de Selberg-Delange”

Plus grand facteur premier de valeurs de polynômes aux entiers

R. de la Bretèche (2015)

Acta Arithmetica

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Let P⁺(n) denote the largest prime factor of the integer n. Using the Heath-Brown and Dartyge methods, we prove that for any even unitary irreducible quartic polynomial Φ with integral coefficients and the associated Galois group isomorphic to V₄, there exists a positive constant $c_{Φ}$ such that the set of integers n ≤ X satisfying $P ⁺ (Φ (n)) \geq X^{1 + c_{Φ}}$ has a positive density. Such a result was recently proved by Dartyge for Φ(n) = n⁴ - n² + 1. There is an appendix written with Jean-François Mestre. ...

Théorèmes de préparation Gevrey et étude de certaines applications formelles

Augustin Mouze (2003)

Annales Polonici Mathematici

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We consider subrings A of the ring of formal power series. They are defined by growth conditions on coefficients such as, for instance, Gevrey conditions. We prove preparation theorems of Malgrange type in these rings. As a consequence we study maps F from $ℂ^{s}$ to $ℂ^{p}$ without constant term such that the rank of the Jacobian matrix of F is equal to 1. Let be a formal power series. If F is a holomorphic map, the following result is well known: ∘ F is analytic implies there exists a convergent...

Généralisation d'un théorème de Haagerup

Ferdaous Kellil, Guy Rousseau (2005)

Studia Mathematica

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Let G be a group of automorphisms of a tree X (with set of vertices S) and H a kernel on S × S invariant under the action of G. We want to give an estimate of the $l^{r}$ -operator norm (1 ≤ r ≤ 2) of the operator associated to H in terms of a norm for H. This was obtained by U. Haagerup when G is the free group acting simply transitively on a homogeneous tree. Our result is valid when X is a locally finite tree and one of the orbits of G is the set of vertices at even distance from a given...

Courbes elliptiques sur ℚ, ayant un point d’ordre 2 rationnel sur ℚ, de conducteur $2^{N} p$

Wilfrid Ivorra

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Let p be a prime number ≥ 29 and N be a positive integer. In this paper, we are interested in the problem of the determination, up to ℚ-isomorphism, of all the elliptic curves over ℚ whose conductor is $2^{N} p$ , with at least one rational point of order 2 over ℚ. This problem was studied in 1974 by B. Setzer in case N = 0. Consequently, in this work we are concerned with the case N ≥ 1. The results presented here are analogous to those obtained by B. Setzer and allow one in practice to find...

Ground states of supersymmetric matrix models

Gian Michele Graf (1998-1999)

Séminaire Équations aux dérivées partielles

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We consider supersymmetric matrix Hamiltonians. The existence of a zero-energy bound state, in particular for the $d = 9$ model, is of interest in M-theory. While we do not quite prove its existence, we show that the decay at infinity such a state would have is compatible with normalizability (and hence existence) in $d = 9$ . Moreover, it would be unique. Other values of $d$ , where the situation is somewhat different, shall also be addressed. The analysis is based on a Born-Oppenheimer approximation....

Espaces de suites réelles complètement métrisables

Pierre Casevitz (2001)

Fundamenta Mathematicae

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Let X be an hereditary subspace of the Polish space $ℝ^{ω}$ of real sequences, i.e. a subspace such that [x = (xₙ)ₙ ∈ X and ∀n, |yₙ| ≤ |xₙ|] ⇒ y = (yₙ)ₙ ∈ X. Does X admit a complete metric compatible with its vector structure? We have two results: ∙ If such an X has a complete metric δ, there exists a unique pair (E,F) of hereditary subspaces with E ⊆ X ⊆ F, (E,δ) complete separable, and F complete maximal in a strong sense. On E and F, the metrics have a simple form, and the spaces E are...

Les types de données syntaxiques du système $ℱ$

Samir Farkh, Karim Nour (2010)

RAIRO - Theoretical Informatics and Applications

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We give in this paper a purely syntactical definition of input and output types of system $ℱ$ . We define the syntactical data types as input and output types. We show that any type with positive quantifiers is a syntactical data type and that an input type is an output type. We give some restrictions on the -elimination rule in order to prove that an output type is an input type.

Complexité et automates cellulaires linéaires

Valérie Berthé (2010)

RAIRO - Theoretical Informatics and Applications

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The aim of this paper is to evaluate the growth order of the complexity function (in rectangles) for two-dimensional sequences generated by a linear cellular automaton with coefficients in $ℤ / l ℤ$ , and polynomial initial condition. We prove that the complexity function is quadratic when is a prime and that it increases with respect to the number of distinct prime factors of .

Derivees tangentielles des fonctions de la classe $^{k, α}$ dans les domaines de type fini de ℂ²

Laurent Verdoucq (2002)

Annales Polonici Mathematici

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Let Ω be a domain of finite type in ℂ² and let f be a function holomorphic in Ω and belonging to $^{k, α} (Ω ̅)$ . We prove the existence of boundary values for some suitable derivatives of f of order greater than k. The gain of derivatives holds in the complex-tangential direction and it is precisely related to the geometry of ∂Ω. Then we prove a property of non-isotropic Hölder regularity for these boundary values. This generalizes some results given by J. Bruna and J. M. Ortega for the unit ball. ...

Quantification pour les paires symétriques et diagrammes de Kontsevich

Alberto S. Cattaneo, Charles Torossian (2008)

Annales scientifiques de l'École Normale Supérieure

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In this article we use the expansion for biquantization described in [7] for the case of symmetric spaces. We introduce a function of two variables $E (X, Y)$ for any symmetric pairs. This function has an expansion in terms of Kontsevich’s diagrams. We recover most of the known results though in a more systematic way by using some elementary properties of this $E$ function. We prove that Cattaneo and Felder’s star product coincides with Rouvière’s for any symmetric pairs. We generalize some of...

Sur la classification des séries discrètes des groupes classiques p-adiques: paramètres de Langlands et exhaustivité

Colette Moeglin (2002)

Journal of the European Mathematical Society

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In this paper, we are giving parameters for discrete series of classical $p$ -adic groups. We first define: the analogous of the Langlands morphism of $W_{F}$ in the $L$ -group, part of the analogous of the character of the centralizer of that morphism and, to supply the missing part of the full definition of that character, the cuspidal support of the representation. Then, we state an hypothesis on the reducibility points for induced of cuspidal representations. And we prove that, under this hypothesis,...

$L^{p} (G, X )$ comme sous-espace complémenté de $L^{q} (G, X) $

Mohammad Daher (2013)

Colloquium Mathematicae

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Let G be a compact metric infinite abelian group and let X be a Banach space. We study the following question: if the dual X* of X does not have the Radon-Nikodym property, is $L^{p} (G, X *)$ complemented in $L^{q} (G, X) *$ , 1 < p ≤ ∞, 1/p + 1/q = 1, or, if p = 1, in the subspace of C(G,X)* consisting of the measures that are absolutely continuous with respect to the Haar measure? We show that the answer is negative if X is separable and does not contain ℓ¹, and if 1 ≤ p < ∞. If p = 1, this answers a question...

Fonctions maximales centrées de Hardy-Littlewood sur les groupes de Heisenberg

Hong-Quan Li (2009)

Studia Mathematica

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By getting uniformly asymptotic estimates for the Poisson kernel on Heisenberg groups $ℍ_{2 n + 1}$ , we prove that there exists a constant A > 0, independent of n ∈ ℕ*, such that for all $f \in L ¹ (ℍ_{2 n + 1})$ , we have ${| | M f | |}_{L^{1, \infty}} \leq A n | | f | | ₁$ , where M denotes the centered Hardy-Littlewood maximal function defined by the Carnot-Carathéodory distance or by the Korányi norm.

Sur les courbes hyperelliptiques cyclotomiques et les équations $x^{p} - y^{p} = c z ²$

Wilfrid Ivorra

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Let p be a prime number ≥ 11 and c be a square-free integer ≥ 3. In this paper, we study the diophantine equation $x^{p} - y^{p} = c z ²$ in the case where p belongs to 11,13,17. More precisely, we prove that for those primes, there is no integer solution (x,y,z) to this equation satisfying gcd(x,y,z) = 1 and xyz ≠ 0 if the integer c has the following property: if ℓ is a prime number dividing c then ℓ ≢ 1 mod p. To obtain this result, we consider the hyperelliptic curves $C_{p} : y ² = Φ_{p} (x)$ and $D_{p} : p y ² = Φ_{p} (x)$ , where $Φ_{p}$ is the pth cyclotomic...

Équations elliptiques non linéaires monotones avec un deuxième membre $L^{1}$ ou mesure

François Murat (1998)

Journées équations aux dérivées partielles

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On considère le problème : $\{\begin{matrix} - div a (x, D u) = f dans Ω, \\ u = 0 sur \partial Ω, \end{matrix}$ où $Ω$ est un ouvert borné de $𝐑^{N}$ , où $a (x, ξ)$ est une fonction de Carathéodory, monotone en $ξ$ , coercive, qui définit un opérateur dans $W_{0}^{1, p} (Ω)$ (avec $1 < p \leq N$ ), et où $f$ appartient à $L^{1} (Ω)$ ou est une mesure bornée sur $Ω$ . On introduit une nouvelle définition de la solution de ce problème, la notion de solution renormalisée (ou entropique), et on montre l’existence d’une telle solution et sa continuité par rapport à $f$ . Quand $f$ appartient à $L^{1} (Ω)$ , on montre en outre...

Idéaux fermés de certaines algèbres de Beurling et application aux opérateurs à spectre dénombrable

Cyril Agrafeuil (2005)

Studia Mathematica

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We denote by the unit circle and by the unit disc of ℂ. Let s be a non-negative real and ω a weight such that $ω (n) = {(1 + n)}^{s}$ (n ≥ 0) and the sequence ${(ω (- n) / {(1 + n)}^{s})}_{n \geq 0}$ is non-decreasing. We define the Banach algebra $A_{ω} () = {f \in () : | | f | |}_{ω} = \sum_{n = - \infty}^{+ \infty} | f ̂ (n) | ω (n) < + \infty$ . If I is a closed ideal of $A_{ω} ()$ , we set $h ⁰ (I) = z \in : f (z) = 0 (f \in I)$ . We describe all closed ideals I of $A_{ω} ()$ such that h⁰(I) is at most countable. A similar result is obtained for closed ideals of the algebra $A ⁺_{s} () = f \in A_{ω} () : f ̂ (n) = 0 (n < 0)$ without inner factor. Then we use this description to establish a link between operators with countable spectrum and interpolating...

Présentation jordanienne de l'algèbre de Weyl A₂

J. Alev, F. Dumas (2001)

Annales Polonici Mathematici

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Let k be a commutative field. For any a,b∈ k, we denote by $J_{a, b} (k)$ the deformation of the 2-dimensional Weyl algebra over k associated with the Jordanian Hecke symmetry with parameters a and b. We prove that: (i) any $J_{a, b} (k)$ can be embedded in the usual Weyl algebra A₂(k), and (ii) $J_{a, b} (k)$ is isomorphic to A₂(k) if and only if a = b.

Semi-stabilité des courbes elliptiques

Nicolas Billerey

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Let K be a finite extension of ℚ₂ complete with a discrete valuation v, K̅ an algebraic closure of K, and $K_{n r}$ its maximal unramified subextension. Let E be an elliptic curve defined over K with additive reduction over K and having an integral modular invariant j. There exists a smallest extension L of $K_{n r}$ over which E has good reduction. For some congruences modulo 12 of the valuation v(j) of j, we give the degree of the extension $L / K_{n r}$ . When K is a quadratic ramified extension of ℚ₂, we determine...

Sur un problème parabolique-elliptique

Philippe Benilan, Petra Wittbold (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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We prove existence (uniqueness is easy) of a weak solution to a boundary value problem for an equation like ${(v - 1)}_{t}^{+} = v_{x x} + F {(v)}_{x}$ where the function $F : ℝ \to ℝ$ is only supposed to be locally lipschitz continuous. In order to replace the lack of compactness in on , we use nonlinear semigroup theory.