# 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.

Original language English 529-536 8 Ramanujan Journal 36 3 https://doi.org/10.1007/s11139-013-9536-5 Published - Apr 2015 Yes