On Rankin-Cohen brackets of Hecke eigenforms and modular forms of half-integral weight
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- by YoungJu Choie, Winfried Kohnen and Yichao Zhang;
- Proc. Amer. Math. Soc. 152 (2024), 5025-5037
- DOI: https://doi.org/10.1090/proc/16970
- Published electronically: October 17, 2024
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Abstract:
We generalize the linear relation formula between the square of normalized Hecke eigenforms of weight $k$ and normalized Hecke eigenforms of weight $2k$, to Rankin-Cohen brackets of general degree. As an ingredient of the proof, we also generalize a formula of Zagier on the Petersson inner product of Rankin-Cohen brackets involving Eisenstein series.References
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Bibliographic Information
- YoungJu Choie
- Affiliation: Department of Mathematics, Pohang University of Science and Technology, Pohang, Republic of Korea
- MR Author ID: 269925
- ORCID: 0000-0002-6806-0822
- Email: yjc@postech.ac.kr
- Winfried Kohnen
- Affiliation: Mathematisches Institut der Universität INF 205, D-69120 Heidelberg, Germany
- MR Author ID: 218211
- Email: winfried@mathi.uni-heidelberg.de
- Yichao Zhang
- Affiliation: MOE-LCSM, School of Mathematics and Statistics, Hunan Normal University, Changsha, Hunan 410081, People’s Republic of China
- MR Author ID: 881604
- Email: yichao.zhang@hunnu.edu.cn
- Received by editor(s): January 3, 2024
- Received by editor(s) in revised form: May 21, 2024
- Published electronically: October 17, 2024
- Additional Notes: The first author was partially supported by NRF 2022R1A2B5B0100187113, BSRI-NRF 2021R1A6A1A10042944, and the third author was partially supported by NSFC 12271123.
- Communicated by: Ling Long
- © Copyright 2024 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 152 (2024), 5025-5037
- MSC (2020): Primary 11F11, 11F37, 11F25
- DOI: https://doi.org/10.1090/proc/16970