On sums of integrals of powers of the zeta-function in short intervals
| dc.creator | Ivić, Aleksandar | |
| dc.date | 2005-12-01 | |
| dc.date | 2005-12-04 | |
| dc.date.accessioned | 2026-07-07T07:39:24Z | |
| dc.date.available | 2026-07-07T07:39:24Z | |
| dc.description | The modified Mellin transform ${\cal Z}_k(s) = \int_1^\infty |ζ({1\over2}+ix|^{2k}x^{-s}{\rm d} x$ ($k\ge1$ is a fixed integer, $s = σ+ it$) is used to obtain estimates for $$ \sum_{r=1}^R\int_{t_r-G}^{t_r+G}|ζ(1/2+it)|^{2k}{\rm d} t\quad(T < t_1 < >... < t_R < 2T), $$ where $t_{r+1} - t_r \ge G (r =1,..., R-1), T^ε\le G \le T^{1-ε$. These results can be used to derive bounds for the moments of $}|ζ(1/2+it)|$. | |
| dc.description | 14 pages | |
| dc.identifier | https://arxiv.org/abs/math/0512016 | |
| dc.identifier | http://arxiv.org/abs/math/0512016 | |
| dc.identifier | "Multiple Dirichlet Series, Automorphic Forms, and Analytic Number Theory", Proc. Symposia Pure Math. , AMS, Providence, vol. 75(2006), 231-242. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/121437 | |
| dc.subject | Number Theory | |
| dc.subject | 11M06 | |
| dc.title | On sums of integrals of powers of the zeta-function in short intervals | |
| dc.type | text |