Siegel modular forms associated to Weil representations: $\operatorname{SL}_2(\mathbb{R}) \& \operatorname{GL}_2(\mathbb{R})$ cases

arXiv (Cornell University) 2026 Preprint Open access

Read full text
Authors: Chun-Hui Wang
Cited by: 0

Abstract

We investigate explicit modular forms of weights $1/2$ and $3/2$-classical, minus, and fermionic theta series-arising from the classical Weil representation associated to $\operatorname{SL}_2(\mathbb{R})$ via the $2$-cocycles of Rao, Kudla, Perrin, Lion--Vergne and Satake--Takase. We reorganize these forms using (tensor) induction, and subsequently extend our study to the similitude group $\operatorname{GL}_2(\mathbb{R})$.

Fields of Study & Subjects

Advanced Algebra and Geometry Algebraic Geometry and Number Theory Advanced Mathematical Identities

Publication details

Journal / source
arXiv (Cornell University)
Publication date
11 February 2026
Language
EN
Document type
Preprint