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Dirichlet’s divisor problem

  • K. Chandrasekharan
Part of the Die Grundlehren der mathematischen Wissenschaften book series (GL, volume 167)

Abstract

Let d(n) denote the number of positive divisors of the positive integer n. Let
$$E(x) = \sum\limits_{n \leqslant x} {d(n) - x\log x - (2\gamma - 1)x,\,x \geqslant 1}$$
where γ is Euler’s constant. It is known, after Dirichlet, that
$$ E(x) = 0({x^{{\frac{1}{2}}}}),\quad as\quad x \to \infty $$

Keywords

Fourier Series Periodic Function Trigonometric Series Chapter Viii Arithmetical Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin · Heidelberg 1970

Authors and Affiliations

  • K. Chandrasekharan
    • 1
  1. 1.Eidgenössische Technische Hochschule ZürichDeutschland

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