T. Kobayashi and M. Pevzner, A short proof for Rankin-Cohen brackets and generating operators, Lie Theory and Its Applications in Physics. LT 2023 (V. Dobrev, ed.), Springer Proceedings in Mathematics & Statistics, vol. 473, Springer, 2025, pp. 3-15, doi: 10.1007/978-981-97-6453-2_1. Available also at arXiv: 2402.05363..

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.

[ DOI | arXiv | preprint version(pdf) ]

© Toshiyuki Kobayashi