The fourth moment of quadratic Dirichlet $L$-Functions II
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909090946482176 |
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| author | Shen, Quanli Stucky, Joshua |
| author_facet | Shen, Quanli Stucky, Joshua |
| contents | We prove an asymptotic formula with four main terms for the fourth moment of quadratic Dirichlet $L$-functions unconditionally. Our proof is based on the work of Li , Soundararajan, and Soundararajan-Young. Our proof requires several new ingredients. These include a modified large sieve estimate for quadratic characters where we consider a fourth moment, rather than a second, as well as observing cross cancellations between diagonal and off-diagonal terms, which involves somewhat delicate combinatorial arguments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_01497 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The fourth moment of quadratic Dirichlet $L$-Functions II Shen, Quanli Stucky, Joshua Number Theory 11M06, 11M50 We prove an asymptotic formula with four main terms for the fourth moment of quadratic Dirichlet $L$-functions unconditionally. Our proof is based on the work of Li , Soundararajan, and Soundararajan-Young. Our proof requires several new ingredients. These include a modified large sieve estimate for quadratic characters where we consider a fourth moment, rather than a second, as well as observing cross cancellations between diagonal and off-diagonal terms, which involves somewhat delicate combinatorial arguments. |
| title | The fourth moment of quadratic Dirichlet $L$-Functions II |
| topic | Number Theory 11M06, 11M50 |
| url | https://arxiv.org/abs/2402.01497 |