DOI QR코드

DOI QR Code

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)
  • Received : 2016.10.06
  • Accepted : 2016.11.30
  • Published : 2016.12.25

Abstract

General summation formula for sums involving ${\sigma}(n)/n$ is expressed with infinite series containing a Bessel function.

Keywords

References

  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. https://doi.org/10.2307/1969455
  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)