Linear independence of periods for the symmetric square $L$-functions
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912498396954624 |
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| author | Ni, Tianyu Xue, Hui |
| author_facet | Ni, Tianyu Xue, Hui |
| contents | For $S_k$, the space of cusp forms of weight $k$ for the full modular group, we first introduce periods on $S_k$ associated to symmetric square $L$-functions. We then prove that for a fixed natural number $n$, if $k$ is sufficiently large relative to $n$, then any $n$ such periods are linearly independent. With some extra assumption, we also prove that for $k\geq e^{12}$, we can always pick up to $\frac{\log k}{4}$ arbitrary linearly independent periods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_17608 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Linear independence of periods for the symmetric square $L$-functions Ni, Tianyu Xue, Hui Number Theory 11F11, 11F67 For $S_k$, the space of cusp forms of weight $k$ for the full modular group, we first introduce periods on $S_k$ associated to symmetric square $L$-functions. We then prove that for a fixed natural number $n$, if $k$ is sufficiently large relative to $n$, then any $n$ such periods are linearly independent. With some extra assumption, we also prove that for $k\geq e^{12}$, we can always pick up to $\frac{\log k}{4}$ arbitrary linearly independent periods. |
| title | Linear independence of periods for the symmetric square $L$-functions |
| topic | Number Theory 11F11, 11F67 |
| url | https://arxiv.org/abs/2507.17608 |