On construit et calcule une fonction génératrice liée aux valeurs spéciales du carré symétrique des formes modulaires. Le théorème principal établit que cette fonction est égale à la série de Jacobi-Eisenstein. Le théorème d’interpolation -adique pour les valeurs spéciales du carré symétrique d’une forme modulaire -ordinaire est prouvé comme corollaire du théorème principal.
The aim of this paper is to construct and calculate generating functions connected with special values of symmetric squares of modular forms. The Main Theorem establishes these generating functions to be Jacobi-Eisenstein series i.e. Eisenstein series among Jacobi forms. A theorem on -adic interpolation of the special values of the symmetric square of a -ordinary modular form is proved as a corollary of our Main Theorem.
@article{AIF_1995__45_3_605_0,
author = {Guerzhoy, Pavel I.},
title = {Jacobi-Eisenstein series and $p$-adic interpolation of symmetric squares of cusp forms},
journal = {Annales de l'Institut Fourier},
pages = {605--624},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {45},
number = {3},
year = {1995},
doi = {10.5802/aif.1467},
mrnumber = {96d:11053},
zbl = {0820.11035},
language = {en},
url = {http://www.numdam.org/articles/10.5802/aif.1467/}
}
TY - JOUR AU - Guerzhoy, Pavel I. TI - Jacobi-Eisenstein series and $p$-adic interpolation of symmetric squares of cusp forms JO - Annales de l'Institut Fourier PY - 1995 SP - 605 EP - 624 VL - 45 IS - 3 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.1467/ DO - 10.5802/aif.1467 LA - en ID - AIF_1995__45_3_605_0 ER -
%0 Journal Article %A Guerzhoy, Pavel I. %T Jacobi-Eisenstein series and $p$-adic interpolation of symmetric squares of cusp forms %J Annales de l'Institut Fourier %D 1995 %P 605-624 %V 45 %N 3 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.1467/ %R 10.5802/aif.1467 %G en %F AIF_1995__45_3_605_0
Guerzhoy, Pavel I. Jacobi-Eisenstein series and $p$-adic interpolation of symmetric squares of cusp forms. Annales de l'Institut Fourier, Tome 45 (1995) no. 3, pp. 605-624. doi : 10.5802/aif.1467. http://www.numdam.org/articles/10.5802/aif.1467/
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