On the Riemann zeta-function and the divisor problem III
| dc.creator | Ivic, Aleksandar | |
| dc.date | 2006-10-18 | |
| dc.date | 2006-10-26 | |
| dc.date.accessioned | 2026-07-07T10:15:46Z | |
| dc.date.available | 2026-07-07T10:15:46Z | |
| dc.description | Let $Δ(x)$ denote the error term in the Dirichlet divisor problem, and $E(T)$ the error term in the asymptotic formula for the mean square of $|ζ(1/2+it)|$. If $E^*(t) = E(t) - 2πΔ^*(t/2π)$ with $Δ^*(x) = -Δ(x) + 2Δ(2x) - {1\over2}Δ(4x)$ and we set $\int_0^T E^*(t) dt = 3πT/4 + R(T)$, then we obtain $$ R(T) = O_ε(T^{593/912+ε}), \int_0^TR^4(t) dt \ll_εT^{3+ε}, $$ and $$ \int_0^TR^2(t) dt = T^2P_3(\log T) + O_ε(T^{11/6+ε}), $$ where $P_3(y)$ is a cubic polynomial in $y$ with positive leading coefficient. | |
| dc.description | 18 pages | |
| dc.identifier | https://arxiv.org/abs/math/0610539 | |
| dc.identifier | http://arxiv.org/abs/math/0610539 | |
| dc.identifier | Annales Univ. Sci. Budapest., Sect. Comp. 29(2008), 3-23 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/173283 | |
| dc.subject | Number Theory | |
| dc.subject | 11N37; 11M06 | |
| dc.title | On the Riemann zeta-function and the divisor problem III | |
| dc.type | text |