Godement--Jacquet L-function and homological theta lifting

Rui Chen; Yufeng Li; Xiaohuan Long; Chenhao Tang; Jialiang Zou

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arXiv · 2507.07531

Godement--Jacquet L-function and homological theta lifting

Rui Chen·Yufeng Li·Xiaohuan Long·Chenhao Tang·Jialiang Zou

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Abstract

In this paper we investigate the theta lifting of type II dual pairs over a non-Archimedean local field, by combining the homological method of Adams--Prasad--Savin and the analytic method of Fang--Sun--Xue. We have three main results: 1. we determine completely the big theta lift of an irreducible representation when its Godement--Jacquet L-function is holomorphic at a critical point; 2. we compute the big theta lift of all characters, hence determine the space of eigendistributions on matrix spaces for all characters; 3. we show that the Weil representation is projective if and only if the dual pair is almost in the stable range.

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BibTeX RIS

Rui Chen, Yufeng Li, Xiaohuan Long, Chenhao Tang, Jialiang Zou. 2025-07-10. Godement--Jacquet L-function and homological theta lifting. https://arxiv.org/abs/2507.07531

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