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

2024/06/20 by Wei Wang, Wang, Wei
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Algebraic structures and combinatorial models

paper · pdf · doi:10.48550/arxiv.2406.14254

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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