Displaying similar documents to “Exponents in Archimedean Arthur packets”

Non-Archimedean K-spaces

Albert Kubzdela (2005)

Banach Center Publications

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We study Banach spaces over a non-spherically complete non-Archimedean valued field K. We prove that a non-Archimedean Banach space over K which contains a linearly homeomorphic copy of l (hence l itself) is not a K-space. We discuss the three-space problem for a few properties of non-Archimedean Banach spaces.

Towards the Jacquet conjecture on the Local Converse Problem for p -adic GL n

Dihua Jiang, Chufeng Nien, Shaun Stevens (2015)

Journal of the European Mathematical Society

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The Local Converse Problem is to determine how the family of the local gamma factors γ ( s , π × τ , ψ ) characterizes the isomorphism class of an irreducible admissible generic representation π of GL n ( F ) , with F a non-archimedean local field, where τ runs through all irreducible supercuspidal representations of GL r ( F ) and r runs through positive integers. The Jacquet conjecture asserts that it is enough to take r = 1 , 2 , ... , n 2 . Based on arguments in the work of Henniart and of Chen giving preliminary steps towards the Jacquet...

Characterizations of Archimedean n -copulas

Włodzimierz Wysocki (2015)

Kybernetika

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We present three characterizations of n -dimensional Archimedean copulas: algebraic, differential and diagonal. The first is due to Jouini and Clemen. We formulate it in a more general form, in terms of an n -variable operation derived from a binary operation. The second characterization is in terms of first order partial derivatives of the copula. The last characterization uses diagonal generators, which are “regular” diagonal sections of copulas, enabling one to recover the copulas by...

A proof of the Grünbaum conjecture

Bruce L. Chalmers, Grzegorz Lewicki (2010)

Studia Mathematica

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Let V be an n-dimensional real Banach space and let λ(V) denote its absolute projection constant. For any N ∈ N with N ≥ n define λ N = s u p λ ( V ) : d i m ( V ) = n , V l ( N ) , λₙ = supλ(V): dim(V) = n. A well-known Grünbaum conjecture [Trans. Amer. Math. Soc. 95 (1960)] says that λ₂ = 4/3. König and Tomczak-Jaegermann [J. Funct. Anal. 119 (1994)] made an attempt to prove this conjecture. Unfortunately, their Proposition 3.1, used in the proof, is incorrect. In this paper a complete proof of the Grünbaum conjecture is presented ...

On the Brocard-Ramanujan problem and generalizations

Andrzej Dąbrowski (2012)

Colloquium Mathematicae

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Let p i denote the ith prime. We conjecture that there are precisely 28 solutions to the equation n ² - 1 = p α p k α k in positive integers n and α₁,..., α k . This conjecture implies an explicit description of the set of solutions to the Brocard-Ramanujan equation. We also propose another variant of the Brocard-Ramanujan problem: describe the set of solutions in non-negative integers of the equation n! + A = x₁²+x₂²+x₃² (A fixed).

On a number theoretic conjecture on positive integral points in a 5-dimensional tetrahedron and a sharp estimate of the Dickman–De Bruijn function

Ke-Pao Lin, Xue Luo, Stephen S.-T. Yau, Huaiqing Zuo (2014)

Journal of the European Mathematical Society

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It is well known that getting the estimate of integral points in right-angled simplices is equivalent to getting the estimate of Dickman-De Bruijn function ψ ( x , y ) which is the number of positive integers x and free of prime factors > y . Motivating from the Yau Geometry Conjecture, the third author formulated the Number Theoretic Conjecture which gives a sharp polynomial upper estimate that counts the number of positive integral points in n-dimensional ( n 3 ) real right-angled simplices. In this...

The Cohen-Lenstra heuristics, moments and p j -ranks of some groups

Christophe Delaunay, Frédéric Jouhet (2014)

Acta Arithmetica

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This article deals with the coherence of the model given by the Cohen-Lenstra heuristic philosophy for class groups and also for their generalizations to Tate-Shafarevich groups. More precisely, our first goal is to extend a previous result due to É. Fouvry and J. Klüners which proves that a conjecture provided by the Cohen-Lenstra philosophy implies another such conjecture. As a consequence of our work, we can deduce, for example, a conjecture for the probability laws of p j -ranks of...

The strength of the projective Martin conjecture

C. T. Chong, Wei Wang, Liang Yu (2010)

Fundamenta Mathematicae

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We show that Martin’s conjecture on Π¹₁ functions uniformly T -order preserving on a cone implies Π¹₁ Turing Determinacy over ZF + DC. In addition, it is also proved that for n ≥ 0, this conjecture for uniformly degree invariant Π ¹ 2 n + 1 functions is equivalent over ZFC to Σ ¹ 2 n + 2 -Axiom of Determinacy. As a corollary, the consistency of the conjecture for uniformly degree invariant Π¹₁ functions implies the consistency of the existence of a Woodin cardinal.

Recent progress on the Jacobian Conjecture

Michiel de Bondt, Arno van den Essen (2005)

Annales Polonici Mathematici

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We describe some recent developments concerning the Jacobian Conjecture (JC). First we describe Drużkowski’s result in [6] which asserts that it suffices to study the JC for Drużkowski mappings of the form x + ( A x ) * 3 with A² = 0. Then we describe the authors’ result of [2] which asserts that it suffices to study the JC for so-called gradient mappings, i.e. mappings of the form x - ∇f, with f k [ n ] homogeneous of degree 4. Using this result we explain Zhao’s reformulation of the JC which asserts the...

Congruences modulo between ϵ factors for cuspidal representations of G L ( 2 )

Marie-France Vignéras (2000)

Journal de théorie des nombres de Bordeaux

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Let p be two different prime numbers, let F be a local non archimedean field of residual characteristic p , and let 𝐐 ¯ , 𝐙 ¯ , 𝐅 ¯ be an algebraic closure of the field of -adic numbers 𝐐 , the ring of integers of 𝐐 ¯ , the residual field of 𝐙 ¯ . We proved the existence and the unicity of a Langlands local correspondence over 𝐅 ¯ for all n 2 , compatible with the reduction modulo in [V5], without using L and ϵ factors of pairs. We conjecture that the Langlands local correspondence over 𝐐 ¯ respects congruences...

A basis of ℤₘ, II

Min Tang, Yong-Gao Chen (2007)

Colloquium Mathematicae

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Given a set A ⊂ ℕ let σ A ( n ) denote the number of ordered pairs (a,a’) ∈ A × A such that a + a’ = n. Erdős and Turán conjectured that for any asymptotic basis A of ℕ, σ A ( n ) is unbounded. We show that the analogue of the Erdős-Turán conjecture does not hold in the abelian group (ℤₘ,+), namely, for any natural number m, there exists a set A ⊆ ℤₘ such that A + A = ℤₘ and σ A ( n ̅ ) 5120 for all n̅ ∈ ℤₘ.

Homotopy invariance of higher signatures and 3 -manifold groups

Michel Matthey, Hervé Oyono-Oyono, Wolfgang Pitsch (2008)

Bulletin de la Société Mathématique de France

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For closed oriented manifolds, we establish oriented homotopy invariance of higher signatures that come from the fundamental group of a large class of orientable 3 -manifolds, including the “piecewise geometric” ones in the sense of Thurston. In particular, this class, that will be carefully described, is the class of all orientable 3 -manifolds if the Thurston Geometrization Conjecture is true. In fact, for this type of groups, we show that the Baum-Connes Conjecture With Coefficients...

A proof of the Livingston conjecture for the fourth and the fifth coefficient of concave univalent functions

Karl-Joachim Wirths (2004)

Annales Polonici Mathematici

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Let D denote the open unit disc and f:D → ℂ̅ be meromorphic and injective in D. We further assume that f has a simple pole at the point p ∈ (0,1) and an expansion f ( z ) = z + n = 2 a ( f ) z , |z| < p. In particular, we consider f that map D onto a domain whose complement with respect to ℂ̅ is convex. Because of the shape of f(D) these functions will be called concave univalent functions with pole p and the family of these functions is denoted by Co(p). It is proved that for p ∈ (0,1) the domain of variability...

Selection principles and upper semicontinuous functions

Masami Sakai (2009)

Colloquium Mathematicae

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In connection with a conjecture of Scheepers, Bukovský introduced properties wQN* and SSP* and asked whether wQN* implies SSP*. We prove it in this paper. We also give characterizations of properties S₁(Γ,Ω) and S f i n ( Γ , Ω ) in terms of upper semicontinuous functions

The H S P -Classes of Archimedean l -groups with Weak Unit

Bernhard Banaschewski, Anthony Hager (2010)

Annales de la faculté des sciences de Toulouse Mathématiques

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W denotes the class of abstract algebras of the title (with homomorphisms preserving unit). The familiar H , S , and P from universal algebra are here meant in W . and denote the integers and the reals, with unit 1, qua W -objects. V denotes a non-void finite set of positive integers. Let 𝒢 W be non-void and not { { 0 } } . We show ...

Entropy of Schur–Weyl measures

Sevak Mkrtchyan (2014)

Annales de l'I.H.P. Probabilités et statistiques

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Relative dimensions of isotypic components of N th order tensor representations of the symmetric group on n letters give a Plancherel-type measure on the space of Young diagrams with n cells and at most N rows. It was conjectured by G. Olshanski that dimensions of isotypic components of tensor representations of finite symmetric groups, after appropriate normalization, converge to a constant with respect to this family of Plancherel-type measures in the limit when N n converges to a constant....