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http://dx.doi.org/10.5831/HMJ.2014.36.2.467

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

Kimy, Insuk (Department of Mathematical education, Wonkwang University)
Cho, Myung Hyun (Department of Mathematical education, Wonkwang University)

Publication Information

Honam Mathematical Journal / v.36, no.2, 2014 , pp. 467-472 More about this Journal

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;

Citations & Related Records

Reference

1	M. Eichler, The basis problem for modular forms and the traces of Hecke operators, Springer-Verlag, Lecture Notes in Math., 320 (1972), 75-151.
2	H. Davenport, Multiplicative number theory, 3rd., Springer-Verlag, 2000.
3	A. Ivic, The Riemann zeta-function, Wiley, 1985.
4	H. Montgomery, Topics in multiplicative number theory, Springer-Verlag, 1971.
5	A. Selberg, Contributions to the theory of the Riemann zeta function, Arch. Math. Naturbid. B 48 (1946), 89-155.
6	A. Selberg An elementary proof of the prime number theorem, Ann. of Math. 50(2) (1949), 305-313.