Rankin-Cohen deformations and representation theory

Abstract

The author uses the unitary representation theory of SL ₂(ℝ) to understand the Rankin-Cohen brackets for modular forms. Then this interpretation is used to study the corresponding deformation problems that Paula Cohen, Yuri Manin and Don Zagier initiated. Two uniqueness results are established.

Keywords

Modular forms / Rankin-Cohen brackets / Representation theory / Rankin-Cohen deformation

References

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