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Ordinary p -adic Eisenstein series and p -adic L -functions for unitary groups

Ming-Lun Hsieh (2011)

Annales de l’institut Fourier

The purpose of this work is to carry out the first step in our four-step program towards the main conjecture for GL 2 × 𝒦 × by the method of Eisenstein congruence on G U ( 3 , 1 ) , where 𝒦 is an imaginary quadratic field. We construct a p -adic family of ordinary Eisenstein series on the group of unitary similitudes G U ( 3 , 1 ) with the optimal constant term which is basically the product of the Kubota-Leopodlt p -adic L -function and a p -adic L -function for GL 2 × 𝒦 × . This construction also provides a different point of view of p -adic...

Ordinary reduction of K3 surfaces

Fedor Bogomolov, Yuri Zarhin (2009)

Open Mathematics

Let X be a K3 surface over a number field K. We prove that there exists a finite algebraic field extension E/K such that X has ordinary reduction at every non-archimedean place of E outside a density zero set of places.

Ordre, convergence et sommabilité de produits de séries de Dirichlet

Jean-Pierre Kahane, Hervé Queffélec (1997)

Annales de l'institut Fourier

L’article donne des réponses optimales ou presque optimales aux questions suivantes, qui remontent à Stieltjes, Landau et Bohr, et concernent des séries de Dirichlet A j = n = 1 a ( j , n ) n - s ( j = 1 , 2 ...

Ordre de grandeur de L ( 1 , χ ) et de L ' ( 1 , χ )

Jean-René Joly, Claude Moser (1979)

Annales de l'institut Fourier

On étudie sommairement la distribution des valeurs de L ' ( 1 , χ ) ( χ : caractère de Dirichlet primitif réel) et on constate qu’on a en général L ' ( 1 , χ ) < π 2 / 6 ; on démontre par ailleurs que si L ' ( 1 , χ ) < ( π 2 / 6 ) - ϵ , alors L ( 1 , χ ) > c ( ϵ ) / log k ( k : conducteur de χ ; c ( ϵ ) : constante positive effectivement calculable.

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