Shimura's Vector-Valued Modular Forms, Weight Changing Operators, and Laplacians

Abstract

We investigate the various types of weight raising and weight lowering operators on quasi-modular forms, or equivalently on Shimura's vector-valued modular forms involving symmetric power representations. We also present all the eigenfunctions of the two possible Laplacian operators.

58 pages, corrected a significant mistake and established the full result about the eigenfunctions

References in corpus (2)

• Regularized Pairings of Meromorphic Modular Forms and Theta Lifts
• On Quasi-Modular Forms, Almost Holomorphic Modular Forms, and the Vector-Valued Modular Forms of Shimura