Correlations of the squares of the Riemann zeta on the critical line
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911764405288960 |
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| author | Kovaleva, Valeriya |
| author_facet | Kovaleva, Valeriya |
| contents | We compute the average of a product of two shifted squares of the Riemann zeta on the critical line with shifts up to size $T^{3/2-\varepsilon}$. We give an explicit expression for such an average and derive an approximate spectral expansion for the error term similar to Motohashi's. As a consequence, we also compute the $(2,2)$-moment of moment of the Riemann zeta, for which we partially verify (and partially refute) a conjecture of Bailey and Keating. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_13725 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Correlations of the squares of the Riemann zeta on the critical line Kovaleva, Valeriya Number Theory We compute the average of a product of two shifted squares of the Riemann zeta on the critical line with shifts up to size $T^{3/2-\varepsilon}$. We give an explicit expression for such an average and derive an approximate spectral expansion for the error term similar to Motohashi's. As a consequence, we also compute the $(2,2)$-moment of moment of the Riemann zeta, for which we partially verify (and partially refute) a conjecture of Bailey and Keating. |
| title | Correlations of the squares of the Riemann zeta on the critical line |
| topic | Number Theory |
| url | https://arxiv.org/abs/2401.13725 |