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

Ming-Lun Hsieh[1]

  • [1] National Taiwan University Department of Mathematics Taipei (Taiwan)

Annales de l’institut Fourier (2011)

  • Volume: 61, Issue: 3, page 987-1059
  • ISSN: 0373-0956

Abstract

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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 L -functions of GL 2 × 𝒦 × .

How to cite

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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 61.3 (2011): 987-1059. <http://eudml.org/doc/219709>.

@article{Hsieh2011,
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 $.},
affiliation = {National Taiwan University Department of Mathematics Taipei (Taiwan)},
author = {Hsieh, Ming-Lun},
journal = {Annales de l’institut Fourier},
keywords = {Eisenstein series on unitary groups; Iwasawa-Greenberg main conjectures; -adic -functions; Selmer group; Shimura variety; Igusa scheme},
language = {eng},
number = {3},
pages = {987-1059},
publisher = {Association des Annales de l’institut Fourier},
title = {Ordinary $p$-adic Eisenstein series and $p$-adic $L$-functions for unitary groups},
url = {http://eudml.org/doc/219709},
volume = {61},
year = {2011},
}

TY - JOUR
AU - Hsieh, Ming-Lun
TI - Ordinary $p$-adic Eisenstein series and $p$-adic $L$-functions for unitary groups
JO - Annales de l’institut Fourier
PY - 2011
PB - Association des Annales de l’institut Fourier
VL - 61
IS - 3
SP - 987
EP - 1059
AB - 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 $.
LA - eng
KW - Eisenstein series on unitary groups; Iwasawa-Greenberg main conjectures; -adic -functions; Selmer group; Shimura variety; Igusa scheme
UR - http://eudml.org/doc/219709
ER -

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