On the higher moments of the error term in the divisor problem
| dc.creator | Ivić, Aleksandar | |
| dc.creator | Sargos, Patrick | |
| dc.date | 2004-11-24 | |
| dc.date.accessioned | 2026-07-07T08:31:35Z | |
| dc.date.available | 2026-07-07T08:31:35Z | |
| dc.description | Let $Δ(x)$ denote the error term in the Dirichlet divisor problem. Our main results are the asymptotic formulas $$ \int_1^X Δ^3(x){\rm d}x = BX^{7/4} + O_ε(X^{β+ε}) \qquad(B > 0) $$ and $$ \int_1^X Δ^4(x){\rm d}x = CX^2 + O_ε(X^{γ+ε}) \qquad(C > 0) $$ with $β= 7/5, γ= 23/12$. This improves on the values $β= 47/28, γ= 45/23$, due to K.-M. Tsang. A result on the integrals of $Δ^3(x)$ and $Δ^4(x)$ in short intervals is also proved. | |
| dc.description | 27 pages | |
| dc.identifier | https://arxiv.org/abs/math/0411537 | |
| dc.identifier | http://arxiv.org/abs/math/0411537 | |
| dc.identifier | Illinois Journal of Mathematics 51(2007), 353-377. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/138542 | |
| dc.subject | Number Theory | |
| dc.subject | 11N37; 11M06 | |
| dc.title | On the higher moments of the error term in the divisor problem | |
| dc.type | text |