Period functions of half-integral weight modular forms
Journal de Théorie des Nombres de Bordeaux, Tome 27 (2015) no. 1, pp. 33-45.

Dans cet article, we étudions la cohomologie d’Eichler associée aux formes cupsidales de poids demi-entiers en utilisant la fonction zêta de Dedekind η(z). Nous montrons que la η-multiplication (resp. θ-multiplication) induit un isomorphisme entre l’espace des formes cupsidales de poids demi-entiers et le groupe de cohomologie associé à l’espace η𝒫 (resp. θ𝒫). Nous montrons aussi qu’il existe un isomorphisme entre la somme directe de deux espaces de telles formes et le groupe de cohomologie.

In this paper, we study the Eichler cohomology associated with half-integral weight cusp forms using the Dedekind eta function η(z) and the theta function θ(z). We prove that η-multiplication (resp. θ-multiplication) gives an isomorphism between the space of cusp forms of a half-integral weight and the cohomology group associated with the space η𝒫 (resp. θ𝒫). We also show that there is an isomorphism between the direct sum of two spaces of cusp forms of half-integral weights and the cohomology group.

Reçu le : 2013-07-29
Accepté le : 2013-11-24
Accepté après révision le : 2013-12-16
Publié le : 2015-05-21
DOI : https://doi.org/10.5802/jtnb.891
Classification : 11F37,  32N10
Mots clés: Period functions, Eichler cohomology
@article{JTNB_2015__27_1_33_0,
     author = {Dohoon Choi and Subong Lim and Wissam Raji},
     title = {Period functions of half-integral weight  modular forms},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
     volume = {27},
     number = {1},
     year = {2015},
     pages = {33-45},
     doi = {10.5802/jtnb.891},
     mrnumber = {3346962},
     language = {en},
     url = {jtnb.centre-mersenne.org/item/JTNB_2015__27_1_33_0/}
}
Dohoon Choi; Subong Lim; Wissam Raji. Period functions of half-integral weight  modular forms. Journal de Théorie des Nombres de Bordeaux, Tome 27 (2015) no. 1, pp. 33-45. doi : 10.5802/jtnb.891. https://jtnb.centre-mersenne.org/item/JTNB_2015__27_1_33_0/

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