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

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.

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.

DOI: 10.5802/jtnb.891
Classification: 11F37,  32N10
Keywords: Period functions, Eichler cohomology
Dohoon Choi 1; Subong Lim 2; Wissam Raji 3

1 School of liberal arts and sciences Korea Aerospace University 200-1, Hwajeon-dong, Goyang Gyeonggi 412-791, Republic of Korea
2 Department of Mathematics Education Sungkyunkwan University Joongno-gu Seoul 110-745, Republic of Korea
3 Department of mathematics American University of Beirut Beirut, Lebanon
     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},
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     publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
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     year = {2015},
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Dohoon Choi; Subong Lim; Wissam Raji. Period functions of half-integral weight  modular forms. Journal de théorie des nombres de Bordeaux, Volume 27 (2015) no. 1, pp. 33-45. doi : 10.5802/jtnb.891.

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