Extreme values of class group $L$-functions
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914025728638976 |
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| author | Campos-Vargas, João |
| author_facet | Campos-Vargas, João |
| contents | We give a lower bound for the maximum value of class group $L$-functions attached to $\mathbb{Q}(\sqrt{-D})$ at the central point and show that this value is on average at least $$\exp\Bigg(δ\sqrt{\frac{\log D \log \log \log D}{\log \log D}} \Bigg)$$ for any $δ< \frac{1}{4}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_05473 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Extreme values of class group $L$-functions Campos-Vargas, João Number Theory We give a lower bound for the maximum value of class group $L$-functions attached to $\mathbb{Q}(\sqrt{-D})$ at the central point and show that this value is on average at least $$\exp\Bigg(δ\sqrt{\frac{\log D \log \log \log D}{\log \log D}} \Bigg)$$ for any $δ< \frac{1}{4}$. |
| title | Extreme values of class group $L$-functions |
| topic | Number Theory |
| url | https://arxiv.org/abs/2509.05473 |