Browse > Article
http://dx.doi.org/10.5831/HMJ.2016.38.4.849

ON THE SUMMATION FORMULA FOR THE CERTAIN ARITHMETIC FUNCTION  

Kim, Insuk (Department of Mathematical education, Wonkwang University)
Jun, Sungtae (College of Liberal arts, Konkuk University)
Publication Information
Honam Mathematical Journal / v.38, no.4, 2016 , pp. 849-856 More about this Journal
Abstract
General summation formula for sums involving ${\sigma}(n)/n$ is expressed with infinite series containing a Bessel function.
Keywords
zeta function; Dirichlet inversion formula; Voronoi formula;
Citations & Related Records
연도 인용수 순위
  • Reference
1 A.L. Dixon and W. L. Ferrar Lattice point summation formulae. Quart.J.Math.(Oxford) , Vol.2, pp.31-54, 1931.
2 K, Chandrasekharan Lectures on The Riemann Zeta-function , Tata institue of fundamental research, 1953.
3 H. Davenport, Multiplicative number theory , 3rd., Springer-Verlag, 2000.
4 A. Ivic, The Riemann zeta-function, Wiley, 1985.
5 M, Kreh, Bessel functions , Project for the Penn state-Gotinggen summer school number theory, 2010.
6 H. Montgomery, Topics in multiplicative number theory, Springer-Verlag, 1971.
7 A. Selberg, Contributions to the theory of the Riemann zeta function, Arch. Math. Naturbid. B Vol.48, pp. 89-155, 1946.
8 A. Selberg, An elementary proof of the prime number theorem, Ann. of Math. Vol. 50(2) , pp. 305-313, 1949.   DOI
9 G.F. Voronoi. Surune fonction transcendante et ses applications a la sommation dequelques series , Ann. Ecole Normale. Vol. 21(3) , pp. 207-268, (1904a). ; Vol. 21(3), 459-534 (1904b)