A discrete mean-value theorem for the higher derivatives of the Riemann zeta function
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2021
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914591710117888 |
|---|---|
| author | Hughes, Christopher Pearce-Crump, Andrew |
| author_facet | Hughes, Christopher Pearce-Crump, Andrew |
| contents | We show that the $n$th derivative of the Riemann zeta function, when summed over the non-trivial zeros of zeta, is real and positive/negative in the mean for $n$ odd/even, respectively. We show this by giving a full asymptotic expansion of these sums. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2106_03005 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | A discrete mean-value theorem for the higher derivatives of the Riemann zeta function Hughes, Christopher Pearce-Crump, Andrew Number Theory 11M06, 11M26 We show that the $n$th derivative of the Riemann zeta function, when summed over the non-trivial zeros of zeta, is real and positive/negative in the mean for $n$ odd/even, respectively. We show this by giving a full asymptotic expansion of these sums. |
| title | A discrete mean-value theorem for the higher derivatives of the Riemann zeta function |
| topic | Number Theory 11M06, 11M26 |
| url | https://arxiv.org/abs/2106.03005 |