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Arxiv.org
by Sary Drappeau
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Dans un r\'ecent article, Lagarias et Soundararajan \'etudient les solutions friables \`a l'\'equation a+b=c. Sous l'hypoth\`ese de Riemann g\'en\'eralis\'ees aux fonctions L de Dirichlet, ils obtiennent une estimation pour le nombre de solutions pond\'er\'ees par un poids lisse et une minoration pour le nombre de solutions non pond\'er\'ees. Le but de cet article est de pr\'esenter des arguments qui permettent d'une part de pr\'eciser les termes d'erreur et d'\'etendre les domaines de...
Source: http://arxiv.org/abs/1203.1742v1
Arxiv.org
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Let $X$ be an analytic space over a non-Archimedean, complete field $k$ and let $(f_1,..., f_n)$ be a family of invertible functions on $X$. Let $\phi$ the morphism $X\to G_m^n$ induced by the $f_i$'s, and let $t$ be the map $X\to (R^*_+)^n$ induced by the norms of the $f_i$'s. Let us recall two results. 1) The compact set $t(X)$ is a polytope of the $R$-vector space $(R^*_+)^n$ (we use the multiplicative notation) ; this is due to Berkovich in the locally algebraic case, and has been extended...
Source: http://arxiv.org/abs/1203.6498v3
Let G be the group GL(N,F), where F is a non-archimedean locally compact field. Using Bushnell and Kutzko's simple types, as well as an original idea of Henniart's, we construct explicit pseudo-coefficients for the discrete series representations of G. As an application we deduce new formulas for the value of the Harish-Chandra character of certain such representations at certain elliptic regular elements.
Source: http://arxiv.org/abs/1203.6788v1
Arxiv.org
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Let F be a finite field and let C be a smooth projective curve over F. For some smooth projective surfaces X over F we establish that the third unramified cohomology of the product of X and C vanishes. This applies in particular to geometrically rational surfaces. Soit F un corps fini et soit C une courbe projective et lisse sur F. Pour certaines surfaces projectives et lisses X sur F on \'etablit la nullit\'e du troisi\`eme groupe de cohomologie non ramifi\'ee du produit de X et C. Cela...
Source: http://arxiv.org/abs/1203.2141v1
Arxiv.org
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Following Steinberg, we construct an adjoint quotient for the Vinberg semi-group and a section to this quotient. Then, after Ng\^o, we show the existence of a regular centralizer on it and use it to compute the affine Springer fibers for groups.
Source: http://arxiv.org/abs/1203.0975v2
Arxiv.org
by Pierre Bonneau; Anne Cumenge
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In the framework of superanalysis we get a functions theory close to complex analysis, under a suitable condition (A) on the real superalgebras in consideration (this condition is a generalization of the classical relation 1 + i^2 = 0 in C). Under the condition (A), we get an integral representation formula for the superdifferentiable functions.We give a result of Hartogs type of separated superdifferentiability, a continuation theorem of Hartogs-Bochner type and a Liouville theorem for the...
Source: http://arxiv.org/abs/1007.0819v2
Arxiv.org
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We consider, on a compact manifold, the group of diffeomorphisms that are isotopic to the identity. We show that every recurrent element is a distorsion element. This generalizes Avila's theorem on circle diffeomorphisms. The method also provides a new proof of a result by Calegari and Freedman: on a sphere, in the group of homeomorphisms that are isotopic to the identity, every element is distorted.
Source: http://arxiv.org/abs/1005.1765v2
Arxiv.org
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In courses on integration theory, Chasles property is usually considered as elementary and so "natural" that this is sometimes left to the reader. When the functions take their values in finite dimensional spaces, the property is always verified, but it no more true in infinite dimensional spaces. We first give an easy-to-understand example of a function f from [-1, 1] into the space of polynomial functions from [0, 1] to R which is integrable on [-1, 1] but not on [0, 1]. We also...
Source: http://arxiv.org/abs/1203.5263v1