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arXiv · 2602.10769

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

Chun-Hui Wang
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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 $\operatorname{GL}_2(\mathbb{R})$.

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Chun-Hui Wang. 2026-02-11. Siegel modular forms associated to Weil representations: $\operatorname{SL}_2(\mathbb{R}) \& \operatorname{GL}_2(\mathbb{R})$ cases. https://arxiv.org/abs/2602.10769

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