English

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

Number Theory 2020-08-13 v2

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.

Keywords

Cite

@article{arxiv.1606.07966,
  title  = {Shimura's Vector-Valued Modular Forms, Weight Changing Operators, and Laplacians},
  author = {Shaul Zemel},
  journal= {arXiv preprint arXiv:1606.07966},
  year   = {2020}
}

Comments

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

R2 v1 2026-06-22T14:34:17.126Z