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Abelian and Tauberian results on Dirichlet series

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Abstract

In this paper, we shall unify the results of Briggs [2] and Buschman [4], under a general Abelian principle, using the slowly oscillating function as a reducing factor. The essential ingredient is that all information arises from the formula for integration by parts for Stieltjes integrals or what amounts eventually to the partial summation.

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Authors and Affiliations

  1. Department of Mathematics, Northwest University Xi’an, Shaanxi, P. R. China

    Liping Ding

  2. Department of Mathematics, Weinan Teacher’s College Weinan, Shaanxi, P. R. China

    Hailong Li

  3. Department of Mathematics, Kagoshima National College of Technology, 1460-1 Shinko, Hayato, Kagoshima 899-51, Japan

    S. Shirasaka

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  1. Liping Ding
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  2. Hailong Li
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  3. S. Shirasaka
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Ding, L., Li, H. & Shirasaka, S. Abelian and Tauberian results on Dirichlet series. Results. Math. 48, 27–33 (2005). https://doi.org/10.1007/BF03322893

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  • DOI: https://doi.org/10.1007/BF03322893

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