Dirichlet’s divisor problem

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


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
$$ E(x) = 0({x^{{\frac{1}{2}}}}),\quad as\quad x \to \infty $$


Fourier Series Periodic Function Trigonometric Series Chapter Viii Arithmetical Function 
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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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