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Ming-Lun Hsieh
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, 61 no. 3 (2011), p. 987-1059, doi: 10.5802/aif.2635
Article: subscription required (your ip address: 54.144.210.245) | Reviews MR 2918724 | Zbl 1271.11051
Class. Math.: 11F33, 11F70, 11R23
Keywords: Eisenstein series on unitary groups, Iwasawa-Greenberg main conjectures

Résumé - Abstract

The purpose of this work is to carry out the first step in our four-step program towards the main conjecture for $\text{GL}_2\times {\mathcal{K}}^\times $ by the method of Eisenstein congruence on $GU(3,1)$, where ${\mathcal{K}}$ 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 $\text{GL}_2\times {\mathcal{K}}^\times $. This construction also provides a different point of view of $p$-adic $L$-functions of $\text{GL}_2\times {\mathcal{K}}^\times $.

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