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Dirichlet series with periodic coefficients

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Abstract

In this paper we shall unify the results obtained so far in various scattered literature, for Dirichlet characters and the associated Dirichlet L-functions, under the paradigm of periodic arithmetic functions and the associated Dirichlet series. Notably we shall determine the Laurent coefficients of the series in question to cover Funakura’s result and proceed on to prove the Ayoub-Berndt-Carlitz-Chowla-Müller-Redmond theorem.

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Authors and Affiliations

  1. Kagoshima Nat’l College of Tech., 1460-1 Shinko Hayato-cho, Kagoshima, 899-51, Japan

    Makoto Ishibashi

  2. Graduate School of Ind. Tech. Univ. of Kinki, Kyushu Campus Iizuka, Fukuoka, 820, Japan

    Shigeru Kanemitsu

Authors
  1. Makoto Ishibashi
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  2. Shigeru Kanemitsu
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Correspondence to Makoto Ishibashi.

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Dedicated to Professor Pan Chengbiao on his 60th birthday

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Ishibashi, M., Kanemitsu, S. Dirichlet series with periodic coefficients. Results. Math. 35, 70–88 (1999). https://doi.org/10.1007/BF03322023

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