On the Riemann zeta-function and the divisor problem IV
| dc.creator | Ivić, Aleksandar | |
| dc.date | 2007-01-07 | |
| dc.date | 2007-01-21 | |
| dc.date.accessioned | 2026-07-07T07:41:49Z | |
| dc.date.available | 2026-07-07T07:41:49Z | |
| 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 $Δ^*(x) = -Δ(x) + 2Δ(2x) - {1\over2}Δ(4x)$, then it is proved that $$ \int_0^T|E^*(t)|^3dt \ll_εT^{3/2+ε}, $$ which is (up to `$ε$' best possible) and $ζ(1/2+it) \ll_εt^{ρ/2+ε}$ if $E^*(t) \ll_εt^{ρ+ε}$. | |
| dc.description | 11 pages | |
| dc.identifier | https://arxiv.org/abs/math/0701202 | |
| dc.identifier | http://arxiv.org/abs/math/0701202 | |
| dc.identifier | Uniform Distribution Theory 1(2006), 125-135 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/122258 | |
| dc.subject | Number Theory | |
| dc.subject | 11N37, 11M06 | |
| dc.title | On the Riemann zeta-function and the divisor problem IV | |
| dc.type | text |