DOI QR코드

DOI QR Code

COMBINATORIC CONVOLUTION SUMS CONTAINING σ AND $\tilde{\sigma}$ OF THE FORM 2mp

  • Received : 2014.07.29
  • Accepted : 2014.08.25
  • Published : 2014.09.25

Abstract

In this paper, we study combinatoric convolution sums of divisor functions and get values of this sum when $n=2^mp$. We find that the value of this convolution sum is represented by a sum of powers of 2 and Bernoulli or Euler number.

Keywords

References

  1. A. Bayad, N. Y. Ikikardes and D. Kim, Certain combinatoric convolution sums and their relations to Bernoulli and Euler polynomials, submitted.
  2. M. Besge, Extrait d'une lettre de M. Besge a M. Liouville, J. Math. Pures Appl. 7 (1862), 256.
  3. B. Cho, D. Kim and H. Park, Evaluation of a certain combinatorial convolution sum in higher level cases, J. Math. Anal. Appl. 406 (2013), 203-210. https://doi.org/10.1016/j.jmaa.2013.04.052
  4. B. Cho, D. Kim and H. Park, Certain combinatorial convolution sums for divisor functions and Bernoulli numbers, Accepted to Bul. Korean Math. Soc.
  5. W. Chu, R. R. Zhou, Convolutions of Bernoulli and Euler polynomials, Sarajevo J. Math. 6(18) (2010), 147-163.
  6. D. Kim and A. Bayad, Convolution identities for twisted Eisenstein series and twisted divisor functions, Fixed Point Theory and Applications, 2013(81) (2013).
  7. D. Kim, A. Bayad and J. Park, Euler polynomials and combinatoric convolution sums of divisor functions with even indices, Abstract and Applied Analysis, accepted and to be published.
  8. S. Ramanujan, On certain arithmetical functions, Trans. Cambridge Philos. Soc., 22 (1916), 159-184.
  9. H. M. Srivastava and A. Pinter, Remarks on some relationships between the Bernoulli and Euler polynomials, Appl. Math. Lett., 17 (2004), 375-380. https://doi.org/10.1016/S0893-9659(04)90077-8