Construction of cusp forms using Rankin-Cohen brackets
Number Theory
2016-07-14 v1
Abstract
For a fix modular form g and a non negative ineteger {\nu}, by using Rankin-Cohen bracket we first define a linear map 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.
Cite
@article{arxiv.1607.03511,
title = {Construction of cusp forms using Rankin-Cohen brackets},
author = {Abhash Kumar Jha and Arvind Kumar},
journal= {arXiv preprint arXiv:1607.03511},
year = {2016}
}