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The adjoint of some linear maps constructed with the Rankin–Cohen brackets

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Abstract

Given a fixed modular form of level 1 we define a family of linear operators between spaces of cusp forms by use of the Rankin–Cohen brackets and we compute the adjoint maps of such family with respect to the usual Petersson inner product. This is done in terms of the effect on the Fourier development of cusp forms. This is a generalization of a result due to W. Kohnen. As an application we prove certain relations among Fourier coefficients of cusp forms.

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Authors and Affiliations

  1. Dept. de Matemática, Fac. de Matemáticas, P. Universidad Católica de Chile, Av. Vicuña Mackenna 4860, Santiago, Chile

    Sebastián Daniel Herrero

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  1. Sebastián Daniel Herrero
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Correspondence to Sebastián Daniel Herrero.

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During the preparation of this paper, the author was partially supported by the Chilean Conicyt and by the Chilean Fondecyt Grant 1121064.

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Herrero, S.D. The adjoint of some linear maps constructed with the Rankin–Cohen brackets. Ramanujan J 36, 529–536 (2015). https://doi.org/10.1007/s11139-013-9536-5

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  • DOI: https://doi.org/10.1007/s11139-013-9536-5

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