The adjointness of the maps between the space of Jacobi forms and the space of modular forms
type: Item
instance of: scholarly article
title: The adjointness of the maps between the space of Jacobi forms and the space of modular forms
zbMATH Open document ID: 0798.11014
author: Yasushi Tokuno
published in: Tôhoku Mathematical Journal. Second Series
publication date: 1994-06-15T00:00:00Z
review text: \textit{M. Eichler} and \textit{D. Zagier} [The theory of Jacobi forms (Prog. Math. 55) (1985; Zbl 0554.10018)] constructed a map from a space of Jacobi forms to a space of elliptic modular forms. On the other hand, \textit{T. Satoh} [Math. Ann. 285, 463-480 (1989; Zbl 0678.10021)] constructed a map from a space of cusp forms to a space of Jacobi cusp forms. In this paper, we prove a conjecture of \textit{N. P. Skoruppa} [J. Reine Angew. Math. 411, 66-95 (1990; Zbl 0702.11028)] to the effect that these maps are, up to constant, adjoint with respect to the Petersson products.
Mathematics Subject Classification ID: 11F50
Mathematics Subject Classification ID: 11F11
zbMATH DE Number: 589800
zbMATH Keywords: adjointness
zbMATH Keywords: Jacobi forms
zbMATH Keywords: elliptic modular forms
zbMATH Keywords: Jacobi cusp forms
zbMATH Keywords: Petersson products
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1178225800
OpenAlex ID: W2064100736
cites work: Q3918184
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cites work: Binary quadratic forms and the Fourier coefficients of elliptic and Jacobi modular forms.
DOI: 10.2748/TMJ/1178225800
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description: scientific article; zbMATH DE number 589800