Sums of the error term function in the mean square for $ζ(s)$
| dc.creator | Bugeaud, Yann | |
| dc.creator | Ivić, Aleksandar | |
| dc.date | 2007-07-29 | |
| dc.date.accessioned | 2026-07-07T10:15:31Z | |
| dc.date.available | 2026-07-07T10:15:31Z | |
| dc.description | Sums of the form $\sum_{n\le x}E^k(n) (k\in{\bf N}$ fixed) are investigated, where $$ E(T) = \int_0^T|ζ(1/2+it)|^2 dt - T\Bigl(\log {T\over2π} + 2γ-1\Bigr)$$ is the error term in the mean square formula for $|ζ(1/2+it)|$. The emphasis is on the case k=1, which is more difficult than the corresponding sum for the divisor problem. The analysis requires bounds for the irrationality measure of ${\rm e}^{2πm}$ and for the partial quotients in its continued fraction expansion. | |
| dc.description | 14 pages | |
| dc.identifier | https://arxiv.org/abs/0707.4275 | |
| dc.identifier | http://arxiv.org/abs/0707.4275 | |
| dc.identifier | Monats. Mathematik, 155(2008), 107-118 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/173197 | |
| dc.subject | Number Theory | |
| dc.subject | 11M06, 11N37, 11J82 | |
| dc.title | Sums of the error term function in the mean square for $ζ(s)$ | |
| dc.type | text |