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ON THE BOUND FOR THE SUM OF THE ABSOLUTE VALUE OF MÖBIUS FUNCTION

Kimy, Insuk;Cho, Myung Hyun

  • Received : 2014.05.09
  • Accepted : 2014.05.31
  • Published : 2014.06.25

Abstract

With the properties of Riemann zeta function, we find an asymptotic formula of the sum for the absolute value of M$\ddot{o}$bius function, $\sum_{n{\leq}x}{\mid}{\mu}(n){\mid}$, using Dirichlet inversion formula.

Keywords

zeta function;Dirichlet inversion formula;Mangoldt function

References

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  6. A. Selberg An elementary proof of the prime number theorem, Ann. of Math. 50(2) (1949), 305-313.

Cited by

  1. ON THE SUM OF CERTAIN MULTIPLICATIVE FUNCTIONS vol.36, pp.3, 2014, https://doi.org/10.5831/HMJ.2014.36.3.689

Acknowledgement

Supported by : Wonkwang University