Construction of cusp forms using Rankin-Cohen brackets

2016/07/12 by Jha, Abhash Kumar, Kumar, Arvind
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1607.03511

Abstract

For a fix modular form g and a non negative ineteger ν, by using Rankin-Cohen bracket we first define a linear map T_g,ν on the space of modular forms. We explicitly compute the adjoint of this map and show that the n-th Fourier coefficients of the image of the cusp form f under this map is, upto a constant a special value of Rankin-Selberg convolution of f and g.

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• Dirichlet series of Rankin-Cohen Brackets