On the characteristic power series of the U operator

Gouvêa, Fernando Q.; Mazur, Barry

doi:10.5802/aif.1332

Gouvêa, Fernando Q. ; Mazur, Barry

Annales de l'Institut Fourier, Tome 43 (1993) no. 2, pp. 301-312.

Résumé
Abstract

Soit $A_{m} (k)$ le coefficient $m$ -ième de la série puissance caractéristique de l’opérateur U de Atkin agissant sur l’espace de formes modulaires $p$ -adiques surconvergentes de poids $k$ ( $k$ entier). Nous montrons que les fonctions $a_{m} (k)$ sont $p$ -adiquement continues en $k$ . Sont-elles des fonctions de Type Iwasawa en $k$ ?

We show that the coefficients of the characteristic power series of Atkin’s U operator acting on overconvergent $p$ -adic modular forms of weight $k$ vary $p$ -adically continuously as functions of $k$ . Are they in fact Iwasawa functions of $k$ ?

EuDML MR Zbl | 2 citations dans Numdam

DOI : 10.5802/aif.1332

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     title = {On the characteristic power series of the {U} operator},
     journal = {Annales de l'Institut Fourier},
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     publisher = {Institut Fourier},
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     volume = {43},
     number = {2},
     year = {1993},
     doi = {10.5802/aif.1332},
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Gouvêa, Fernando Q.; Mazur, Barry. On the characteristic power series of the U operator. Annales de l'Institut Fourier, Tome 43 (1993) no. 2, pp. 301-312. doi : 10.5802/aif.1332. http://www.numdam.org/articles/10.5802/aif.1332/

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