Ordinary p-adic Eisenstein series and p-adic L-functions for unitary groups
[Les séries d’Eisenstein ordinaires p-adiques et la fonction L p-adique pour les groupes unitaires]
Annales de l'Institut Fourier, Tome 61 (2011) no. 3, pp. 987-1059.

Le but de ce travail est d’accomplir le premier pas de notre programme vers la conjecture principale pour GL 2 ×𝒦 × , par la methode de congruences entre séries d’Eisenstein sur GU(3,1), où 𝒦 est d’un corps quadratique imaginaire. Nous construisons une famille p-adique de séries d’Eisenstein ordinaires sur le groupe de similitudes unitaires avec le terme constant optimal qui est essentiellement le produit de la fonction L p-adique de Kubota-Leopoldt et d’une fonction L p-adique pour GL 2 ×𝒦 × . Cette construction donne ainsi un nouveau point de vue sur la fonction L p-adique de GL 2 ×𝒦 × .

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 GU(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 GU(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 L-functions of GL 2 ×𝒦 × .

DOI : 10.5802/aif.2635
Classification : 11F33, 11F70, 11R23
Keywords: Eisenstein series on unitary groups, Iwasawa-Greenberg main conjectures
Mot clés : Les séries d’Eisenstein sur les groupes unitaires, la conjecture principale de Iwasawa-Greenberg
Hsieh, Ming-Lun 1

1 National Taiwan University Department of Mathematics Taipei (Taiwan)
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Hsieh, Ming-Lun. Ordinary $p$-adic Eisenstein series and $p$-adic $L$-functions for unitary groups. Annales de l'Institut Fourier, Tome 61 (2011) no. 3, pp. 987-1059. doi : 10.5802/aif.2635. http://www.numdam.org/articles/10.5802/aif.2635/

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