Ikehara-type theorem involving boundedness
| dc.creator | Korevaar, Jacob | |
| dc.date | 2008-07-03 | |
| dc.date.accessioned | 2026-07-07T09:48:14Z | |
| dc.date.available | 2026-07-07T09:48:14Z | |
| dc.description | Consider any Dirichlet series sum a_n/n^z with nonnegative coefficients a_n and finite sum function f(z)=f(x+iy) when x is greater than 1. Denoting the partial sum a_1+...+a_N by s_N, the paper gives the following necessary and sufficient condition in order that (s_N)/N remain bounded as N goes to infinity. For x tending to 1 from above, the quotient q(x+iy)=f(x+iy)/(x+iy) must converge to a pseudomeasure q(1+iy), the distributional Fourier transform of a bounded function. The paper also gives an optimal estimate for (s_N)/N under the "real condition" that (1-x)f(x) remain bounded as x tends to 1 from above. | |
| dc.description | 6 pages | |
| dc.identifier | https://arxiv.org/abs/0807.0537 | |
| dc.identifier | http://arxiv.org/abs/0807.0537 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/164136 | |
| dc.subject | Number Theory | |
| dc.subject | 40E05 | |
| dc.title | Ikehara-type theorem involving boundedness | |
| dc.type | text |