We address some questions posed by Goss related to the modularity of Drinfeld modules of rank
For each positive characteristic valued Dirichlet character, we introduce certain projection operators on spaces of Drinfeld modular forms with character of a given weight and type such that when applied to a Hecke eigenform return a Hecke eigenform whose eigensystem has been twisted by the given Dirichlet character. Unlike the classical case, however, the effect on Goss’
We also introduce Eisenstein series with character for irreducible levels
Nous considérons des questions posées par Goss concernant la modularité des modules de Drinfeld de rang un définis sur le corps des fonctions rationnelles en une variable, avec coefficients dans un corps fini.
Pour chaque caractère de Dirichlet à valeurs dans un corps fini, nous introduisons des opérateurs de projection sur des espaces de formes modulaires de Drinfeld avec caractère, de poids et type donnés. Ces opérateurs envoient des formes propres pour les opérateurs de Hecke sur des formes propres de Hecke, dont le système de valeurs propres est tordu par le caractère de Dirichlet. À la différence du cas classique, l’effet de ces opérateurs sur les
Nous introduisons aussi des séries d’Eisenstein avec caractère, avec niveau irréductible
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Keywords: A-expansions, twisting, congruences, Eisenstein series, Drinfeld modular forms, modularity
Rudolph Perkins 1

@article{JTNB_2017__29_3_903_0, author = {Rudolph Perkins}, title = {Twisting eigensystems of {Drinfeld} {Hecke} eigenforms by characters}, journal = {Journal de th\'eorie des nombres de Bordeaux}, pages = {903--929}, publisher = {Soci\'et\'e Arithm\'etique de Bordeaux}, volume = {29}, number = {3}, year = {2017}, doi = {10.5802/jtnb.1006}, language = {en}, url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1006/} }
TY - JOUR AU - Rudolph Perkins TI - Twisting eigensystems of Drinfeld Hecke eigenforms by characters JO - Journal de théorie des nombres de Bordeaux PY - 2017 SP - 903 EP - 929 VL - 29 IS - 3 PB - Société Arithmétique de Bordeaux UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1006/ DO - 10.5802/jtnb.1006 LA - en ID - JTNB_2017__29_3_903_0 ER -
%0 Journal Article %A Rudolph Perkins %T Twisting eigensystems of Drinfeld Hecke eigenforms by characters %J Journal de théorie des nombres de Bordeaux %D 2017 %P 903-929 %V 29 %N 3 %I Société Arithmétique de Bordeaux %U https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1006/ %R 10.5802/jtnb.1006 %G en %F JTNB_2017__29_3_903_0
Rudolph Perkins. Twisting eigensystems of Drinfeld Hecke eigenforms by characters. Journal de théorie des nombres de Bordeaux, Tome 29 (2017) no. 3, pp. 903-929. doi : 10.5802/jtnb.1006. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1006/
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