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dc.contributor.authorKnill, Oliver
dc.contributor.authorLesieutre, John D
dc.date.accessioned2016-12-01T19:33:10Z
dc.date.available2016-12-01T19:33:10Z
dc.date.issued2010-04
dc.date.submitted2010-03
dc.identifier.issn1661-8254
dc.identifier.issn1661-8262
dc.identifier.urihttp://hdl.handle.net/1721.1/105497
dc.description.abstractWe 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.publisherSP Birkhäuser Verlag Baselen_US
dc.relation.isversionofhttp://dx.doi.org/10.1007/s11785-010-0064-7en_US
dc.rightsArticle 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.sourceSP Birkhäuser Verlag Baselen_US
dc.titleAnalytic Continuation of Dirichlet Series with Almost Periodic Coefficientsen_US
dc.typeArticleen_US
dc.identifier.citationKnill, 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.departmentMassachusetts Institute of Technology. Department of Mathematicsen_US
dc.contributor.mitauthorLesieutre, John D
dc.relation.journalComplex Analysis and Operator Theoryen_US
dc.eprint.versionAuthor's final manuscripten_US
dc.type.urihttp://purl.org/eprint/type/JournalArticleen_US
eprint.statushttp://purl.org/eprint/status/PeerRevieweden_US
dc.date.updated2016-08-18T15:40:41Z
dc.language.rfc3066en
dc.rights.holderBirkhäuser / Springer Basel AG
dspace.orderedauthorsKnill, Oliver; Lesieutre, Johnen_US
dspace.embargo.termsNen
mit.licensePUBLISHER_POLICYen_US


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