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Unimodalité de la distribution du nombre de diviseurs premiers d'un entier

Michel Balazard (1990)

Annales de l'institut Fourier

Pour $x$ assez grand, le nombre de diviseurs premiers de $n$ , $1 \leq n \leq x$ , a une distribution locale unimodale. Cela confirme une conjecture d’Erdös de 1948.

Unimodality of certain sequences connected with binomial coefficients.

Belbachir, Hacéne, Bencherif, Farid, Szalay, László (2007)

Journal of Integer Sequences [electronic only]

Unimodular brackets and related structures

Wolfgang Rump (2005)

Acta Arithmetica

Unimodular covers of multiples of polytopes.

Bruns, Winfried, Gubeladze, Joseph (2002)

Documenta Mathematica

Unimodular lattices over real quadratic fields.

Rudolf Scharlau (1994)

Mathematische Zeitschrift

Unimodular Pisot substitutions and their associated tiles

Jörg M. Thuswaldner (2006)

Journal de Théorie des Nombres de Bordeaux

Let $σ$ be a unimodular Pisot substitution over a $d$ letter alphabet and let $X_{1}, ..., X_{d}$ be the associated Rauzy fractals. In the present paper we want to investigate the boundaries $\partial X_{i}$ ( $1 \leq i \leq d$ ) of these fractals. To this matter we define a certain graph, the so-called contact graph $𝒞$ of $σ$ . If $σ$ satisfies a combinatorial condition called the super coincidence condition the contact graph can be used to set up a self-affine graph directed system whose attractors are certain pieces of the boundaries $\partial X_{1}, ..., \partial X_{d}$ . From this graph...

Unipotent orbital integrals of spherical functions on p-adic 4 X 4 symplectic groups.

Magdy Assem (1993)

Journal für die reine und angewandte Mathematik

Unipotent vector bundles and higher-order non-holomorphic Eisenstein series

Jay Jorgenson, Cormac O’Sullivan (2008)

Journal de Théorie des Nombres de Bordeaux

Higher-order non-holomorphic Eisenstein series associated to a Fuchsian group $Γ$ are defined by twisting the series expansion for classical non-holomorphic Eisenstein series by powers of modular symbols. Their functional identities include multiplicative and additive factors, making them distinct from classical Eisenstein series. In this article we prove the meromorphic continuation of these series and establish their functional equations which relate values at $s$ and $1 - s$ . In addition, we construct...