Petersson norms of Eisenstein series and Kohnen–Zagier’s formula

Yoshinori Mizuno

doi:10.5802/jtnb.1138

Yoshinori Mizuno

Journal de Théorie des Nombres de Bordeaux, Tome 32 (2020) no. 3, pp. 665-684.

Résumé
Abstract

Les normes de Petersson régularisées des séries d’Eisenstein de poids entier et demi-entier sont calculées. Nous utilisons ces résultats pour établir la formule de Kohnen–Zagier pour les séries d’Eisenstein.

The regularized Petersson norms of Eisenstein series of integral and half-integral weight are computed. We use these results to establish Kohnen–Zagier’s formula for Eisenstein series.

Reçu le : 2018-10-25
Révisé le : 2020-07-03
Accepté le : 2020-09-18
Publié le : 2021-01-08

DOI : https://doi.org/10.5802/jtnb.1138
Classification : 11F37, 11F11
Mots clés : Petersson norms, Eisenstein series, Kohnen–Zagier’s formula

@article{JTNB_2020__32_3_665_0,
     author = {Yoshinori Mizuno},
     title = {Petersson norms of Eisenstein series and Kohnen--Zagier's formula},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {665--684},
     publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
     volume = {32},
     number = {3},
     year = {2020},
     doi = {10.5802/jtnb.1138},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/item/JTNB_2020__32_3_665_0/}
}

Yoshinori Mizuno. Petersson norms of Eisenstein series and Kohnen–Zagier’s formula. Journal de Théorie des Nombres de Bordeaux, Tome 32 (2020) no. 3, pp. 665-684. doi : 10.5802/jtnb.1138. https://jtnb.centre-mersenne.org/item/JTNB_2020__32_3_665_0/

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