aequationes mathematicae

, Volume 53, Issue 1–2, pp 73–90 | Cite as

Arithmetical sequences and systems of functional equations

  • Lutz G. Lucht
Research Papers
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Summary

This note investigates the arithmetic origin and structure of functional equations of the type
$$\frac{1}{n}\sum\limits_{v - 0}^{n - 1} {G(e^{2\pi iv/n} z) = \sum\limits_{d = 1}^\infty {\lambda _n (d)G(z^{nd} )} } $$
with naturaln and complexz, and the closely related
$$\frac{1}{n}\sum\limits_{v - 0}^{n - 1} {F\left( {\frac{{x + v}}{n}} \right) = \sum\limits_{d = 1}^\infty {\lambda _n (d)F(dx)} } $$
with realx. We establish some fundamental results concerning their holomorphic, their periodic integrable and their aperiodic continuous solutions, respectively. The main tools are of number theoretic and functional analytic nature.

AMS (1991) subject classification

Primary 39B62 secondary 11A25 
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Copyright information

© Birkhäuser Verlag 1997

Authors and Affiliations

  • Lutz G. Lucht
    • 1
  1. 1.Institut für MathematikTechnische Universität ClausthalClausthal-ZellerfeldGermany

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