On p-adic L-functions of GL(2)×GL(2) over totally real fields
Hida, Haruzo
Annales de l'Institut Fourier, Tome 41 (1991), p. 311-391 / Harvested from Numdam
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Soit D(s,f,g) le produit de Rankin de deux formes paraboliques hilbertiennes f et g. Cette fonction L est en fait la fonction L standard d’une représentation automorphe du groupe algébrique GL(2)×GL(2) défini sur un corps totalement réel. En supposant que f et g sont ordinaires en p, nombre premier, nous allons construire une fonction analytique p-adique de plusieurs variables qui interpole la partie algébrique de D(m,f,g) pour des entiers m critiques en considérant m, f et g comme variables.

Let D(s,f,g) be the Rankin product L-function for two Hilbert cusp forms f and g. This L-function is in fact the standard L-function of an automorphic representation of the algebraic group GL(2)×GL(2) defined over a totally real field. Under the ordinarity assumption at a given prime p for f and g, we shall construct a p-adic analytic function of several variables which interpolates the algebraic part of D(m,f,g) for critical integers m, regarding all the ingredients m, f and g as variables.

@article{AIF_1991__41_2_311_0,
     author = {Hida, Haruzo},
     title = {On $p$-adic $L$-functions of $GL(2)\times GL(2)$ over totally real fields},
     journal = {Annales de l'Institut Fourier},
     volume = {41},
     year = {1991},
     pages = {311-391},
     doi = {10.5802/aif.1258},
     mrnumber = {93b:11052},
     zbl = {0739.11019},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_1991__41_2_311_0}
}

Hida, Haruzo. On $p$-adic $L$-functions of $GL(2)\times GL(2)$ over totally real fields. Annales de l'Institut Fourier, Tome 41 (1991) pp. 311-391. doi : 10.5802/aif.1258. http://gdmltest.u-ga.fr/item/AIF_1991__41_2_311_0/

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