On the moments of averages of quadratic twists of the Möbius function
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929363641958400 |
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| author | Toma, Yuichiro |
| author_facet | Toma, Yuichiro |
| contents | We consider the moment of quadratic twists of the Möbius function of the form \[
S_k(X,Y) = \sum_{d\leq X} \left( \sum_{n\leq Y} \left(\frac{8d}{n}\right) μ(n)\right)^k, \] where $\left(\frac{8d}{\cdot}\right)$ is the Kronecker symbol and $d$ runs over positive, odd and square-free integers. We give unconditional results for their asymptotic behaviors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_18778 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the moments of averages of quadratic twists of the Möbius function Toma, Yuichiro Number Theory We consider the moment of quadratic twists of the Möbius function of the form \[ S_k(X,Y) = \sum_{d\leq X} \left( \sum_{n\leq Y} \left(\frac{8d}{n}\right) μ(n)\right)^k, \] where $\left(\frac{8d}{\cdot}\right)$ is the Kronecker symbol and $d$ runs over positive, odd and square-free integers. We give unconditional results for their asymptotic behaviors. |
| title | On the moments of averages of quadratic twists of the Möbius function |
| topic | Number Theory |
| url | https://arxiv.org/abs/2405.18778 |