Integral moment of the Riemann zeta function and Hecke $L$ functions
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915102997872640 |
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| author | Chen, Zhaoyan |
| author_facet | Chen, Zhaoyan |
| contents | Let $f$ be a Hecke cusp form for $SL(2,\mathbb{Z})$. We prove an asymptotic formula for the mixed moment of the product of $ζ(s)$ and $L(s,f)$ on the critical line. Similarly, we prove an asymptotic formula for the mixed moment of the product of $|ζ^{2}(s)|$ and $L(s,f)$ on the critical line. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_04348 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Integral moment of the Riemann zeta function and Hecke $L$ functions Chen, Zhaoyan Number Theory Let $f$ be a Hecke cusp form for $SL(2,\mathbb{Z})$. We prove an asymptotic formula for the mixed moment of the product of $ζ(s)$ and $L(s,f)$ on the critical line. Similarly, we prove an asymptotic formula for the mixed moment of the product of $|ζ^{2}(s)|$ and $L(s,f)$ on the critical line. |
| title | Integral moment of the Riemann zeta function and Hecke $L$ functions |
| topic | Number Theory |
| url | https://arxiv.org/abs/2501.04348 |