On the Second Moment of Twisted Higher Degree $L$-functions
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911151792586752 |
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| author | Gou, Haozhe Li, Liangxun |
| author_facet | Gou, Haozhe Li, Liangxun |
| contents | Assuming the Ramanujan conjecture, the zero density estimate and some subconvexity type bound, we describe a general method to obtain the log-saving upper bound for the second moment of standard twisted higher degree $L$-function in the $q$-aspect. Specifically, let $L(s, F)$ be a standard $L$-function of degree $d\geq3$. Under these foundational hypotheses. the bound \[ \sideset{}{^*}{\sum}_{χ\pmod q}\Big|L\big(\frac{1}{2}, F\times χ\big)\Big |^2\ll_{F,η} \frac{q^{\frac{d}{2}}}{\log^ηq} \] holds for some small $η>0$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_20144 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Second Moment of Twisted Higher Degree $L$-functions Gou, Haozhe Li, Liangxun Number Theory Assuming the Ramanujan conjecture, the zero density estimate and some subconvexity type bound, we describe a general method to obtain the log-saving upper bound for the second moment of standard twisted higher degree $L$-function in the $q$-aspect. Specifically, let $L(s, F)$ be a standard $L$-function of degree $d\geq3$. Under these foundational hypotheses. the bound \[ \sideset{}{^*}{\sum}_{χ\pmod q}\Big|L\big(\frac{1}{2}, F\times χ\big)\Big |^2\ll_{F,η} \frac{q^{\frac{d}{2}}}{\log^ηq} \] holds for some small $η>0$ |
| title | On the Second Moment of Twisted Higher Degree $L$-functions |
| topic | Number Theory |
| url | https://arxiv.org/abs/2410.20144 |