On the second integral moment of $L$-functions
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866918476543688704 |
|---|---|
| author | Li, Liangxun |
| author_facet | Li, Liangxun |
| contents | Assume that the generalized Ramanujan conjecture holds on the automorphic $L$-function $L(s, π)$ on $\GL_d$ over $\mathbb{Q}$ with $d\geq 3$, we can obtain a small log-saving non-trivial bound on the second integral moment of $L(1/2+it, π)$. Specifically the bound
\[
\int_{T}^{2T}\Big|L\big(\frac{1}{2}+it, π\big)\Big |^2 \dd t\ll_π \frac{T^{\frac{d}{2}}}{\log^{η_d}T}
\] holds for a small constant $η_d>0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_20342 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the second integral moment of $L$-functions Li, Liangxun Number Theory Assume that the generalized Ramanujan conjecture holds on the automorphic $L$-function $L(s, π)$ on $\GL_d$ over $\mathbb{Q}$ with $d\geq 3$, we can obtain a small log-saving non-trivial bound on the second integral moment of $L(1/2+it, π)$. Specifically the bound \[ \int_{T}^{2T}\Big|L\big(\frac{1}{2}+it, π\big)\Big |^2 \dd t\ll_π \frac{T^{\frac{d}{2}}}{\log^{η_d}T} \] holds for a small constant $η_d>0$. |
| title | On the second integral moment of $L$-functions |
| topic | Number Theory |
| url | https://arxiv.org/abs/2410.20342 |