dc.contributor.author | Knill, Oliver | |
dc.contributor.author | Lesieutre, John D | |
dc.date.accessioned | 2016-12-01T19:33:10Z | |
dc.date.available | 2016-12-01T19:33:10Z | |
dc.date.issued | 2010-04 | |
dc.date.submitted | 2010-03 | |
dc.identifier.issn | 1661-8254 | |
dc.identifier.issn | 1661-8262 | |
dc.identifier.uri | http://hdl.handle.net/1721.1/105497 | |
dc.description.abstract | We consider Dirichlet series ζ[subscript g,α](s)=∑[∞ over n=1]g(nα)e[superscript −λ[subscript n]s] for fixed irrational α and periodic functions g. We demonstrate that for Diophantine α and smooth g, the line Re(s) = 0 is a natural boundary in the Taylor series case λ[subscript n] = n, so that the unit circle is the maximal domain of holomorphy for the almost periodic Taylor series ∑[∞ over n=1]g(nα)z[superscript n] . We prove that a Dirichlet series ζ[subscript g,α](s)=∑[∞ over n=1](nα)/n[superscript s] has an abscissa of convergence σ[subscript 0] = 0 if g is odd and real analytic and α is Diophantine. We show that if g is odd and has bounded variation and α is of bounded Diophantine type r, the abscissa of convergence σ[subscript 0] satisfies σ[subscript 0] ≤ 1 − 1/r. Using a polylogarithm expansion, we prove that if g is odd and real analytic and α is Diophantine, then the Dirichlet series ζ[subscript g,α](s) has an analytic continuation to the entire complex plane. | en_US |
dc.publisher | SP Birkhäuser Verlag Basel | en_US |
dc.relation.isversionof | http://dx.doi.org/10.1007/s11785-010-0064-7 | en_US |
dc.rights | Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. | en_US |
dc.source | SP Birkhäuser Verlag Basel | en_US |
dc.title | Analytic Continuation of Dirichlet Series with Almost Periodic Coefficients | en_US |
dc.type | Article | en_US |
dc.identifier.citation | Knill, Oliver, and John Lesieutre. “Analytic Continuation of Dirichlet Series with Almost Periodic Coefficients.” Complex Anal. Oper. Theory 6, no. 1 (April 9, 2010): 237–255. | en_US |
dc.contributor.department | Massachusetts Institute of Technology. Department of Mathematics | en_US |
dc.contributor.mitauthor | Lesieutre, John D | |
dc.relation.journal | Complex Analysis and Operator Theory | en_US |
dc.eprint.version | Author's final manuscript | en_US |
dc.type.uri | http://purl.org/eprint/type/JournalArticle | en_US |
eprint.status | http://purl.org/eprint/status/PeerReviewed | en_US |
dc.date.updated | 2016-08-18T15:40:41Z | |
dc.language.rfc3066 | en | |
dc.rights.holder | Birkhäuser / Springer Basel AG | |
dspace.orderedauthors | Knill, Oliver; Lesieutre, John | en_US |
dspace.embargo.terms | N | en |
mit.license | PUBLISHER_POLICY | en_US |