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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On the analytic continuation of Dirichlet series

Author: Ronald Seeling
Journal: Proc. Amer. Math. Soc. 69 (1978), 119-124
MSC: Primary 30A16
MathSciNet review: 0466504
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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}$.

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  • [1] Ludwig Bieberbach, Analytische Fortsetzung, Ergebnisse der Mathematik und ihrer Grenzgebiete (N.F.), Heft 3, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1955 (German). MR 0068621
  • [2] Alexander Ostrowski, Über die analytische Fortsetzung von Taylorschen und Dirichletschen Reihen, Math. Ann. 129 (1955), 1–43 (German). MR 0069878
  • [3] S. Mandelbrojt, Dirichlet series, D. Reidel Publishing Co., Dordrecht, 1972. Principles and methods. MR 0435370

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Keywords: Dirichlet series, analytic continuation along paths
Article copyright: © Copyright 1978 American Mathematical Society