On the mean square of the zeta-function and the divisor problem
| dc.creator | Ivić, Aleksandar | |
| dc.date | 2006-03-21 | |
| dc.date | 2006-12-26 | |
| dc.date.accessioned | 2026-07-07T07:37:08Z | |
| dc.date.available | 2026-07-07T07:37:08Z | |
| 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 we obtain the asymptotic formula $$ \int_0^T (E^*(t))^2 {\rm d} t = T^{4/3}P_3(\log T) + O_ε(T^{7/6+ε}), $$ where $P_3$ is a polynomial of degree three in $\log T$ with positive leading coefficient. The exponent 7/6 in the error term is the limit of the method. | |
| dc.description | 10 pages | |
| dc.identifier | https://arxiv.org/abs/math/0603491 | |
| dc.identifier | http://arxiv.org/abs/math/0603491 | |
| dc.identifier | Annales Acad. Sci. Fennicae Math. 32(2007), 1-9 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/120668 | |
| dc.subject | Number Theory | |
| dc.subject | 11N37; 11M06 | |
| dc.title | On the mean square of the zeta-function and the divisor problem | |
| dc.type | text |