# Representations of SL_2(R) and nearly holomorphic modular forms

@article{Pitale2015RepresentationsOS, title={Representations of SL_2(R) and nearly holomorphic modular forms}, author={Ameya Pitale and Abhishek Saha and Ralf Schmidt}, journal={arXiv: Number Theory}, year={2015} }

In this semi-expository note, we give a new proof of a structure theorem due to Shimura for nearly holomorphic modular forms on the complex upper half plane. Roughly speaking, the theorem says that the space of all nearly holomorphic modular forms is the direct sum of the subspaces obtained by applying appropriate weight-raising operators on the spaces of holomorphic modular forms and on the one-dimensional space spanned by the weight 2 nearly holomorphic Eisenstein series.
While Shimura's… CONTINUE READING

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## Nearly holomorphic automorphic forms on $\mathrm{SL}_2$

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