Ordinary p-adic Eisenstein series and p-adic L-functions for unitary groups
Annales de l'Institut Fourier, Volume 61 (2011) no. 3, p. 987-1059

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 × .

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 × .

DOI : https://doi.org/10.5802/aif.2635
Classification:  11F33,  11F70,  11R23
Keywords: Eisenstein series on unitary groups, Iwasawa-Greenberg main conjectures
@article{AIF_2011__61_3_987_0,
     author = {Hsieh, Ming-Lun},
     title = {Ordinary $p$-adic Eisenstein series and $p$-adic $L$-functions for unitary groups},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {61},
     number = {3},
     year = {2011},
     pages = {987-1059},
     doi = {10.5802/aif.2635},
     mrnumber = {2918724},
     zbl = {1271.11051},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2011__61_3_987_0}
}
Hsieh, Ming-Lun. Ordinary $p$-adic Eisenstein series and $p$-adic $L$-functions for unitary groups. Annales de l'Institut Fourier, Volume 61 (2011) no. 3, pp. 987-1059. doi : 10.5802/aif.2635. http://www.numdam.org/item/AIF_2011__61_3_987_0/

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