On the search of genuine $p$-adic modular $L$-functions for $GL(n)$. With a correction to : on $p$-adic $L$-functions of $GL(2)\times {}GL(2)$ over totally real fields

The purpose of this monograph is to state several conjectures concerning the existence and the meromorphy of many variable $p$ -adic $L$ -functions attached to many variable Galois representations (for example having values in $G L_{n} (ℤ_{p} [[X_{1}, \dots, X_{r}]])$ ) and to present some supporting examples for the conjectures. Our discussion in the earlier sections is therefore quite speculative, but towards the end, we gradually make things more concrete.

Le but de cette monographie est de formuler quelques conjectures concernant l'existence et la méromorphie des fonctions $L$ $p$ -adiques de plusieurs variables attachées à des représentations galoisiennes de plusieurs variables (par exemple, à valeurs dans $G L_{n} (ℤ_{p} [[X_{1}, \dots, X_{r}]])$ ) et de présenter quelques exemples motivant nos conjectures. Nous commençons par une discussion assez spéculative, mais vers la fin, nous donnons des résultat plus concrets.

Zbl

DOI : 10.24033/msmf.381

Classification : 11F13, 11F41, 11F67, 11F70, 11F85

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     author = {Hida, Haruzo},
     title = {On the search of genuine $p$-adic modular $L$-functions for $GL(n)$. {With} a correction to : on $p$-adic $L$-functions of $GL(2)\times {}GL(2)$ over totally real fields},
     series = {M\'emoires de la Soci\'et\'e Math\'ematique de France},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {67},
     year = {1996},
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     zbl = {0897.11015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/MSMF_1996_2_67__R1_0/}
}

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Hida, Haruzo. On the search of genuine $p$-adic modular $L$-functions for $GL(n)$. With a correction to : on $p$-adic $L$-functions of $GL(2)\times {}GL(2)$ over totally real fields. Mémoires de la Société Mathématique de France, Nouvelle série, no. 67 (1996), 116 p. doi: 10.24033/msmf.381

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