On the joint second moment of zeta and its logarithmic derivative
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910466508324864 |
|---|---|
| author | Fazzari, Alessandro |
| author_facet | Fazzari, Alessandro |
| contents | Assuming the Riemann Hypothesis, Goldston, Gonek and Montgomery \cite{GGM} studied the second moment of the log-derivative of $ζ$, shifted away from the half line by $a/\log T$, and its connection with the pair correlation conjecture. In this paper, we consider a weighted version of this problem, where the average is tilted by $|ζ(\frac{1}{2}+it)|^2$. More precisely, we provide an upper and a lower bound for the second moment of zeta times its logarithmic derivative, $a/\log T$ away from the critical line. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_15918 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the joint second moment of zeta and its logarithmic derivative Fazzari, Alessandro Number Theory 11M06, 11M26 Assuming the Riemann Hypothesis, Goldston, Gonek and Montgomery \cite{GGM} studied the second moment of the log-derivative of $ζ$, shifted away from the half line by $a/\log T$, and its connection with the pair correlation conjecture. In this paper, we consider a weighted version of this problem, where the average is tilted by $|ζ(\frac{1}{2}+it)|^2$. More precisely, we provide an upper and a lower bound for the second moment of zeta times its logarithmic derivative, $a/\log T$ away from the critical line. |
| title | On the joint second moment of zeta and its logarithmic derivative |
| topic | Number Theory 11M06, 11M26 |
| url | https://arxiv.org/abs/2310.15918 |