Le but de ce travail est d’accomplir le premier pas de notre programme vers la conjecture principale pour , par la methode de congruences entre séries d’Eisenstein sur , où est d’un corps quadratique imaginaire. Nous construisons une famille -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 -adique de Kubota-Leopoldt et d’une fonction -adique pour . Cette construction donne ainsi un nouveau point de vue sur la fonction -adique de .
The purpose of this work is to carry out the first step in our four-step program towards the main conjecture for by the method of Eisenstein congruence on , where is an imaginary quadratic field. We construct a -adic family of ordinary Eisenstein series on the group of unitary similitudes with the optimal constant term which is basically the product of the Kubota-Leopodlt -adic -function and a -adic -function for . This construction also provides a different point of view of -adic -functions of .
Classification : 11F33, 11F70, 11R23
Mots clés : Les séries d’Eisenstein sur les groupes unitaires, la conjecture principale de Iwasawa-Greenberg
@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}, pages = {987--1059}, publisher = {Association des Annales de l'institut Fourier}, volume = {61}, number = {3}, year = {2011}, doi = {10.5802/aif.2635}, mrnumber = {2918724}, zbl = {1271.11051}, language = {en}, url = {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, Tome 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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