JOURNAL BROWSE
Search
Advanced SearchSearch Tips
A PRODUCT FORMULA FOR COMBINATORIC CONVOLUTION SUMS OF ODD DIVISOR FUNCTIONS
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
  • Journal title : Honam Mathematical Journal
  • Volume 38, Issue 2,  2016, pp.243-257
  • Publisher : The Honam Mathematical Society
  • DOI : 10.5831/HMJ.2016.38.2.243
 Title & Authors
A PRODUCT FORMULA FOR COMBINATORIC CONVOLUTION SUMS OF ODD DIVISOR FUNCTIONS
Lee, Kwangchul; Kim, Daeyeoul; Seo, Gyeong-Sig;
  PDF(new window)
 Abstract
If we let with , then we get the formula of L(2u; p)L(2v; p)L(2w; p).
 Keywords
Divisor functions;Convolution sums;Bernoulli polynomials;
 Language
English
 Cited by
 References
1.
A. Alaca, S. Alaca, and K. S. Williams, The convolution sum ${{\Sigma}_{l+24m=n}}^{{\sigma}(l){\sigma}(m)}$ and ${{\Sigma}_{3l+8m=n}}^{{\sigma}(l){\sigma}(m)}$, Math. J. Okayama Univ. 49 (2007), 93-111.

2.
A. Alaca, S. Alaca, and K. S. Williams, The convolution sum ${\Sigma}_{m{<}{\frac{n}{16}}^{{\sigma}(m){\sigma}(n-16m)}$, Canad. Math. Bull. 51 (2008), no. 1, 3-14. crossref(new window)

3.
B. C. Berndt, Ramanujan's Notebooks. Part II, Springer-Verlag, New York, 1989.

4.
Dario Castellanos, A note on bernoulli polynomials, Univ. de Carabobo, Valencia, Venezuela (1989), 98-102.

5.
J. W. L. Glaisher, On the square of the series in which the coefficients are the sums of the divisors of the exponents, Mess. Math. 14 (1884), 156-163.

6.
J. W. L. Glaisher, On certain sums of products of quantities depending upon the divisors of a number, Mess. Math. 15 (1885), 1-20.

7.
J. W. L. Glaisher, Expressions for the five powers of the series in which the coefficients are the sums of the divisors of the exponents, Mess. Math. 15 (1885), 33-36.

8.
H. Hahn, Convolution sums of some functions on divisors, Rocky Mountain J. Math. 37 (2007), no. 5, 1593-1622. crossref(new window)

9.
J. G. Huard, Z. M. Ou, B. K. Spearman, and K. S. Williams, Elementary evaluation of certain convolution sums involving divisor functions, Number theory for the millennium, II (Urbana, IL, 2000), 229-274, A K Peters, Natick, MA, 2002.

10.
D. Kim, A. Bayad, and N. Y. Ikikardes, Certain combinatoric convolution sums and their relations to Bernoulli and Euler Polynomials, J. Korean Math. Soc. 52 (2015), No. 3, pp. 537-565. crossref(new window)

11.
K. S. Williams, Number Theory in the Spirit of Liouville, London Mathematical Society, Student Texts 76, Cambridge, 2011.