Let and be holomorphic common eigenforms of all Hecke operators for the congruence subgroup of with “Nebentypus” character and and of weight and , respectively. Define the Rankin product of and by
Supposing and to be ordinary at a prime , we shall construct a -adically analytic -function of three variables which interpolate the values for integers with by regarding all the ingredients , and as variables. Here is the Petersson self-inner product of .
Soient et deux formes paraboliques pour le sous-groupe de , propre pour tous les opérateurs de Hecke, de caractère respectivement et , de poids et . Définissons le produit de Rankin de et par la formule
En supposant que et sont ordinaires en , nombre premier , nous allons construire une fonction analytique -adique de trois variables qui interpole les valeurs
en regardant tous les ingrédients comme variables, où est le produit de Petersson de .
@article{AIF_1988__38_3_1_0, author = {Hida, Haruzo}, title = {A $p$-adic measure attached to the zeta functions associated with two elliptic modular forms. {II}}, journal = {Annales de l'Institut Fourier}, pages = {1--83}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {38}, number = {3}, year = {1988}, doi = {10.5802/aif.1141}, mrnumber = {89k:11120}, zbl = {0645.10028}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.1141/} }
TY - JOUR AU - Hida, Haruzo TI - A $p$-adic measure attached to the zeta functions associated with two elliptic modular forms. II JO - Annales de l'Institut Fourier PY - 1988 SP - 1 EP - 83 VL - 38 IS - 3 PB - Institut Fourier PP - Grenoble UR - http://www.numdam.org/articles/10.5802/aif.1141/ DO - 10.5802/aif.1141 LA - en ID - AIF_1988__38_3_1_0 ER -
%0 Journal Article %A Hida, Haruzo %T A $p$-adic measure attached to the zeta functions associated with two elliptic modular forms. II %J Annales de l'Institut Fourier %D 1988 %P 1-83 %V 38 %N 3 %I Institut Fourier %C Grenoble %U http://www.numdam.org/articles/10.5802/aif.1141/ %R 10.5802/aif.1141 %G en %F AIF_1988__38_3_1_0
Hida, Haruzo. A $p$-adic measure attached to the zeta functions associated with two elliptic modular forms. II. Annales de l'Institut Fourier, Volume 38 (1988) no. 3, pp. 1-83. doi : 10.5802/aif.1141. http://www.numdam.org/articles/10.5802/aif.1141/
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