On the Size of \(\sum\limits_{\text{n} \leqslant \text{x}} {\text{d(n)e(nx)}}\)

  • Takeshi Kano
Part of the Progress in Mathematics book series (PM, volume 70)


In his famous Habilitationsschrift of 1854 on trigonometric series and integration theory, Riemann gave the following interesting example which shows his high ingenuity of analysis and arithmetic as well.


Infinite Series Riemann Function Diophantine Approximation Tauberian Theorem Continue Fraction Expansion 
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Copyright information

© Birkhäuser Boston 1987

Authors and Affiliations

  • Takeshi Kano
    • 1
  1. 1.Okayama UniversityOkayamaJapan

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