A note on the Laplace transform of the square in the circle problem
| dc.creator | Ivić, Aleksandar | |
| dc.date | 2003-12-12 | |
| dc.date.accessioned | 2026-07-07T05:03:52Z | |
| dc.date.available | 2026-07-07T05:03:52Z | |
| dc.description | If $P(x)$ is the error term in the circle problem, then it is proved that $$\int_0^\infty P^2(x)e^{-x/T}dx = {1\over4}({T\overπ})^{3/2} \sum_{n=1}^\infty r^2(n)n^{-3/2} - T + O_ε(T^{2/3+ε}), $$ improving the author's earlier exponent 5/6. The new bound is obtained by using results of F. Chamizo on the correlated sum $\sum_{n\le x}r(n)r(n+h)$, where $r(n)$ is the number of representations of $n$ as a sum of two squares. | |
| dc.description | 8 pages | |
| dc.identifier | https://arxiv.org/abs/math/0312255 | |
| dc.identifier | http://arxiv.org/abs/math/0312255 | |
| dc.identifier | Studia Scientiarum Mathematicarum Hungarica 37(2001), 391-399 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69584 | |
| dc.subject | Number Theory | |
| dc.subject | 11N37; 44A10 | |
| dc.title | A note on the Laplace transform of the square in the circle problem | |
| dc.type | text |