A short proof for Rankin--Cohen brackets and generating operators
Representation Theory
2025-06-16 v2 Classical Analysis and ODEs
Number Theory
Abstract
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.
Keywords
Cite
@article{arxiv.2402.05363,
title = {A short proof for Rankin--Cohen brackets and generating operators},
author = {Toshiyuki Kobayashi and Michael Pevzner},
journal= {arXiv preprint arXiv:2402.05363},
year = {2025}
}