Landau-Siegel Zeros of Triple Product L-functions
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866915716256497664 |
|---|---|
| author | Zhao, Shifan |
| author_facet | Zhao, Shifan |
| contents | Let $F$ be a number field. Let $π_1,π_2$ be cuspidal automorphic representations of $GL_2(\mathbb{A}_F)$, and let $π$ be a cuspidal automorphic representation of either $GL_2(\mathbb{A}_F)$ or $GL_3(\mathbb{A}_F)$. When $(π_1,π_2,π)$ is of general type, we show that the triple product $L$-function $L(s,π_1 \times π_2 \times π)$ on either $GL(2) \times GL(2) \times GL(2)$ or $GL(2) \times GL(2) \times GL(3)$ has a standard zero-free region with no exceptional Landau-Siegel zero. Moreover, when $(π_1,π_2,π)$ is not of general type, we give precise conditions when $L(s,π_1 \times π_2 \times π)$ could possibly have exceptional Landau-Siegel zeros. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_06423 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Landau-Siegel Zeros of Triple Product L-functions Zhao, Shifan Number Theory 11F41, 11F66 Let $F$ be a number field. Let $π_1,π_2$ be cuspidal automorphic representations of $GL_2(\mathbb{A}_F)$, and let $π$ be a cuspidal automorphic representation of either $GL_2(\mathbb{A}_F)$ or $GL_3(\mathbb{A}_F)$. When $(π_1,π_2,π)$ is of general type, we show that the triple product $L$-function $L(s,π_1 \times π_2 \times π)$ on either $GL(2) \times GL(2) \times GL(2)$ or $GL(2) \times GL(2) \times GL(3)$ has a standard zero-free region with no exceptional Landau-Siegel zero. Moreover, when $(π_1,π_2,π)$ is not of general type, we give precise conditions when $L(s,π_1 \times π_2 \times π)$ could possibly have exceptional Landau-Siegel zeros. |
| title | Landau-Siegel Zeros of Triple Product L-functions |
| topic | Number Theory 11F41, 11F66 |
| url | https://arxiv.org/abs/2508.06423 |