Shimura lift of Rankin-Cohen brackets of eigenforms and theta series

Wei Wang

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arXiv · 2406.14254

Shimura lift of Rankin-Cohen brackets of eigenforms and theta series

Wei Wang

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Abstract

The Shimura lift of a Hekce eigenform multiplied by a theta series is the square of the form. We extend this result by generalizing the product map to the Rankin-Cohen bracket. We prove that the Shimura lift of Rankin-Cohen bracket of an eigenform and a theta series is given by Rankin-Cohen bracket of the eigenform and itself.

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Wei Wang. 2024-06-20. Shimura lift of Rankin-Cohen brackets of eigenforms and theta series. https://arxiv.org/abs/2406.14254

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