A PRODUCT FORMULA FOR COMBINATORIC CONVOLUTION SUMS OF ODD DIVISOR FUNCTIONS

• 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;

Abstract
If we let $L(2K;n): Keywords Divisor functions;Convolution sums;Bernoulli polynomials; Language English Cited by References 1. A. Alaca, S. Alaca, and K. S. Williams, The convolution sum${{\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.

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.

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.

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