Analytic continuation of Dirichlet series with almost periodic coefficients
| dc.creator | Knill, Oliver | |
| dc.creator | Lesieutre, John | |
| dc.date | 2008-11-09 | |
| dc.date.accessioned | 2026-07-07T10:17:08Z | |
| dc.date.available | 2026-07-07T10:17:08Z | |
| dc.description | We prove that an ordinary Dirichlet series with coefficients a(n)=g(n b) has an abscissa of convergence 0 if g is an odd 1-periodic, real-analytic function and b is Diophantine. We also show that if g is odd and has bounded variation and b is of bounded Diophantine type r>1, then the abscissa of convergence is smaller or equal than 1-1/r. Using a polylogarithm expansion, we prove that if g is odd and real analytic and b is Diophantine, then the ordinary Dirichlet series has an analytic continuation to the entire complex plane. | |
| dc.description | 15 pages | |
| dc.identifier | https://arxiv.org/abs/0811.1362 | |
| dc.identifier | http://arxiv.org/abs/0811.1362 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/173753 | |
| dc.subject | Complex Variables | |
| dc.subject | 11M99; 30D99; 33E20 | |
| dc.title | Analytic continuation of Dirichlet series with almost periodic coefficients | |
| dc.type | text |