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On the analytic continuation of Dirichlet series


Author: Ronald Seeling
Journal: Proc. Amer. Math. Soc. 69 (1978), 119-124
MSC: Primary 30A16
DOI: https://doi.org/10.1090/S0002-9939-1978-0466504-9
MathSciNet review: 0466504
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Abstract | References | Similar Articles | Additional Information

Abstract: Given a continuable Dirichlet series, having as sequence of exponents $ \{ {\lambda _n}\} _{n = 1}^\infty $, it is shown that any other Dirichlet series can be continued along the same paths away from its half plane of convergence provided that the two series have the same coefficients and that the difference of their exponents is eventually given by a function analytic at infinity evaluated at the $ {\lambda _n}$.


References [Enhancements On Off] (What's this?)

  • [1] L. Bieberbach, Analytische Fortsetzung, Springer, Berlin, 1955. MR 0068621 (16:913a)
  • [2] A. Ostrowski, Über die analytische Fortsetzung von Taylorschen und Dirichletschen Riehen, Math. Ann. 129 (1955), 1-43. MR 0069878 (16:1094a)
  • [3] S. Mandelbrojt, Dirichlet series, D. Reidel Publishing Company, Dordrecht-Holland, 1972. MR 0435370 (55:8330)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1978-0466504-9
Keywords: Dirichlet series, analytic continuation along paths
Article copyright: © Copyright 1978 American Mathematical Society

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