Abstract
Here we obtain the meromorphic continuation of some classical Dirichlet series by means of elementary and simple translation formulae for these series. We are also able to determine the poles and the residues by this method. The motivation to our work originates from an idea of Ramanujan which he used to derive the meromorphic continuation of the Riemann zeta function.
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Acknowledgements
The author would like to thank Sanoli Gun and Purusottam Rath for their helpful comments on an earlier version of this article. He would also like to thank the referee for his/her important comments which improved the readability of this article.
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Communicating Editor: B Sury
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SAHA, B. An elementary approach to the meromorphic continuation of some classical Dirichlet series. Proc Math Sci 127, 225–233 (2017). https://doi.org/10.1007/s12044-017-0327-6
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DOI: https://doi.org/10.1007/s12044-017-0327-6