The moments of the Riemann zeta-function. Part I: The fourth moment off the critical line
| dc.creator | Ivić, Aleksandar | |
| dc.creator | Motohashi, Yoichi | |
| dc.date | 2004-08-02 | |
| dc.date.accessioned | 2026-07-07T07:38:42Z | |
| dc.date.available | 2026-07-07T07:38:42Z | |
| dc.description | In this paper, the first part of a larger work, we prove the spectral decomposition of $$ \int_{-\infty}^\infty|ζ(\s+it)|^4g(t){\rm d}t\qquad(\hf < σ< 1 {\rm {fixed}}), $$ where $g(t)$ is a suitable weight function of fast decay. This is used to obtain estimates and omega results for the function $$\eqalign{E_2(T,σ) &: =\int_0^T|ζ(σ+it)|^4{rm d}t - {ζ^4(2σ)\overζ(4σ)}T -{T\over3-4σ}{({T\over2π} )}^{2-4σ}{ζ^4(2-2σ)\overζ(4-4σ)}\cr& - T^{2-2σ}(a_0(σ) + a_1(σ)\log T + a_2(σ)\log^2T),\cr} $$ the error term in the asymptotic formula for the fourth moment of $|ζ(σ+it)|$. | |
| dc.description | 50 pages | |
| dc.identifier | https://arxiv.org/abs/math/0408022 | |
| dc.identifier | http://arxiv.org/abs/math/0408022 | |
| dc.identifier | Functiones et Approximatio 35(2006), 133-181. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/121184 | |
| dc.subject | Number Theory | |
| dc.subject | 11M06; 11F72, 11F66 | |
| dc.title | The moments of the Riemann zeta-function. Part I: The fourth moment off the critical line | |
| dc.type | text |