1 |
A. Alaca, S. Alaca, and K. S. Williams, The convolution sum ${\Sigma}_{m
DOI
|
2 |
A. Alaca, S. Alaca, and K. S. Williams, The convolution sum and , Math. J. Okayama Univ. 49 (2007), 93-111.
|
3 |
B. C. Berndt, Ramanujan's Notebooks. Part II, Springer-Verlag, New York, 1989.
|
4 |
B. Cho, D. Kim, and J.-K. Koo, Divisor functions arising from q-series, Publ. Math. Debrecen 76(3-4) (2010), 495-508.
|
5 |
B. Cho, D. Kim, and J.-K. Koo, Modula forms arising from divisor functions, J. Math. Anal. Appl. 356(2) (2009), 537-547.
DOI
ScienceOn
|
6 |
J. W. L. Glaisher, On the square of the series in which the coeffcients are the sums of the divisors of the exponents, Mess. Math. 14 (1884), 156-163.
|
7 |
J. W. L. Glaisher, On certain sums of products of quantities depending upon the divisors of a number, Mess. Math. 15 (1885), 1-20.
|
8 |
J. W. L. Glaisher, Expressions for the five powers of the series in which the coeffcients are the sums of the divisors of the exponents, Mess. Math. 15 (1885), 33-36.
|
9 |
H. Hahn, Convolution sums of some functions on divisors, Rocky Mountain J. Math. 37 (2007), 1593-1622.
DOI
ScienceOn
|
10 |
A. Kim, D. Kim and L. Yan, Convolution sums arising from divisor functions, J. Korean Math. Soc. 50 (2013), 331-360.
과학기술학회마을
DOI
ScienceOn
|
11 |
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.
|
12 |
D. Kim, A. Kim, and H. Park, Congruences of the Weierstrass and -Functions on divisors, Bull. Korean Math. Soc. 50 (2013), 241-261.
과학기술학회마을
DOI
ScienceOn
|
13 |
D. Kim, A. Kim, and A. Sankaranarayanan, Eisenstein seires and their applications to some arithmetic identities and congruences, Advances in Difference Equations 2013, 2013:84.
|
14 |
S. Lang, elliptic Functions, Addison-Wesly, 1973.
|
15 |
Erin McAfee, A three term arithmetic formula of liouville type with application to sums of six squares, B. Math.(Honors), Carleton University, 2004.
|
16 |
G. Melfi, On some modular identities, Number theory (Eger, 1996), 371-382, de Gruyter, Berlin, 1998, 371-382.
|