Analytic continuation of a class of Dirichlet series

Peter Grabner; Jörg Thuswaldner

doi:10.1007/BF02940810

Analytic continuation of a class of Dirichlet series

Peter Grabner, Jörg Thuswaldner

Institute of Analysis and Number Theory (5010)

Research output: Contribution to journal › Article › peer-review

Abstract

We consider Dirichlet series of the type Σ(logk)n(k)(logk)ϑ-s. We prove the existence of an analytic continuation to the cut plane and give exact information about the singularity. We use this to generalize results, which occur in Ramanujan’s second notebook.

Original language	English
Pages (from-to)	281-287
Journal	Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
Volume	66
DOIs	https://doi.org/10.1007/BF02940810
Publication status	Published - 1996

Treatment code (Nähere Zuordnung)

Basic - Fundamental (Grundlagenforschung)

Access to Document

10.1007/BF02940810

Cite this

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title = "Analytic continuation of a class of Dirichlet series",

abstract = "We consider Dirichlet series of the type Σ(logk)n(k)(logk)ϑ-s. We prove the existence of an analytic continuation to the cut plane and give exact information about the singularity. We use this to generalize results, which occur in Ramanujan{\textquoteright}s second notebook.",

author = "Peter Grabner and J{\"o}rg Thuswaldner",

year = "1996",

doi = "10.1007/BF02940810",

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journal = "Abhandlungen aus dem Mathematischen Seminar der Universit{\"a}t Hamburg",

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AU - Grabner, Peter

AU - Thuswaldner, Jörg

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AB - We consider Dirichlet series of the type Σ(logk)n(k)(logk)ϑ-s. We prove the existence of an analytic continuation to the cut plane and give exact information about the singularity. We use this to generalize results, which occur in Ramanujan’s second notebook.

U2 - 10.1007/BF02940810

DO - 10.1007/BF02940810

M3 - Article

SN - 1865-8784

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EP - 287

JO - Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg

JF - Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg

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