Weighted inversion of general Dirichlet series
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- by Helge Glöckner and Lutz G. Lucht PDF
- Trans. Amer. Math. Soc. 366 (2014), 3275-3293 Request permission
Abstract:
Inversion theorems of Wiener type are essential tools in analysis and number theory. We derive a weighted version of an inversion theorem of Wiener type for general Dirichlet series from that of Edwards from 1957, and we outline an alternative proof based on the duality theory of convex cones and extension techniques for characters of semigroups. Variants and arithmetical applications are described, including the case of multidimensional weighted generalized Dirichlet series.References
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Additional Information
- Helge Glöckner
- Affiliation: Institut für Mathematik, Universität Paderborn, Warburger Str. 100, D-33098 Paderborn, Germany
- MR Author ID: 614241
- Email: glockner@math.upb.de
- Lutz G. Lucht
- Affiliation: Institut für Mathematik, Technische Universität Clausthal, Erzstr. 1, D-38678 Clausthal-Zellerfeld, Germany
- Email: lg.lucht@cintech.de
- Received by editor(s): December 3, 2011
- Received by editor(s) in revised form: August 3, 2012, and November 13, 2012
- Published electronically: November 5, 2013
- Additional Notes: The first author was supported by Deutsche Forschungsgemeinschaft, GZ: GL 357/5–2.
- © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 366 (2014), 3275-3293
- MSC (2010): Primary 11M41; Secondary 30B50, 30J99, 46H99
- DOI: https://doi.org/10.1090/S0002-9947-2013-06018-7
- MathSciNet review: 3180747