A short proof for Rankin–Cohen brackets and generating operators

Kavli Affiliate: Toshiyuki Kobayashi

| First 5 Authors: Toshiyuki Kobayashi, Michael Pevzner, , ,

| Summary:

Motivated by the concept of "generating operators" for a countable family of
operators introduced in the recent paper (arXiv:2306.16800), we find a method
to reconstruct the Rankin–Cohen brackets from a very simple multivariable
contour integral, and obtain a new proof of their covariance. We also establish
a closed formula of the "generating operator" for the Rankin–Cohen brackets in
full generality.

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