1 |
A. Bazso, A. Pinter, and H. M. Srivastava, A refinement of Faulhaber's theorem concerning sums of powers of natural numbers, Appl. Math. Lett. 25 (2012), no. 3, 486-489.
DOI
ScienceOn
|
2 |
B. C. Berndt, Ramanujan's Notebooks. Part II, Springer-Verlag, New York, 1989.
|
3 |
M. Besge, Extrait d'une lettre de M. Besge a M. Liouville, J. Math. Pures Appl. 7 (1862), 256.
|
4 |
B. Cho, D. Kim, and H. Park, Evaluation of a certain combinatorial convolution sum in higher level cases, J. Math. Anal. Appl. 406 (2013), no. 1, 203-210.
DOI
ScienceOn
|
5 |
W. Chu and R. R. Zhou, Convolutions of Bernoulli and Euler polynomials, Sarajevo J. Math. 6(19) (2010), no. 2, 147-163.
|
6 |
A. Erdelyi, Higher Transcendental Functions. Vol 1, McGraw Hill, New York, 1953.
|
7 |
J. W. L. Glaisher, On the square of the series in which the coefficients are the sums of the divisors of the exponents, Messenger Math. 14 (1885), 156-163.
|
8 |
H. Hahn, Convolution sums of some functions on divisors, Rocky Mountain J. Math. 37 (2007), no. 5, 1593-1622.
DOI
ScienceOn
|
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 and A. Bayad, Convolution identities for twisted Eisenstein series and twisted divisor functions, Fixed Point Theory Appl. 2013 (2013), 81, 23 pp.
|
11 |
D. Kim and N. Y. Ikikardes, Certain combinatoric Bernoulli polynomials and convolution sums of divisor functions, Adv. Difference Equ. 2013 (2013), 310, 11 pp.
|
12 |
A. Kim, D. Kim, and L. Yan, Convolution sums arising from divisor functions, J. Korean Math. Soc. 50 (2013), no. 2, 331-360.
DOI
ScienceOn
|
13 |
D. Kim and Y. K. Park, Bernoulli identities and combinatoric convolution sums with odd divisor functions, Abstr. Appl. Anal. 2014 (2014), Article ID 890973, 8 pages.
|
14 |
L. Navas, F. J. Ruiz, and J. L. Varona, Old and new identities for Bernoulli polynomials via Fourier series, Int. J. Math. Math. Sci. 2012 (2012), Article ID 129126, 14 pp.
|
15 |
D. Kim and Y. K. Park, Certain Combinatoric convolution sums involving divisor functions product formulae, Taiwanese J. Math. 18 (2014), no. 3, 973-988.
DOI
|
16 |
D. B. Lahiri, On Ramanujan's function (n) and the divisor function (n). I, Bull. Calcutta Math. Soc. 38 (1946), 193-206.
|
17 |
G. Melfi, On some modular identities, Number Theory (Eger, 1996), 371-382, de Gruyter, Berlin, 1998.
|
18 |
S. Ramanujan, On certain arithmetical functions, Trans. Cambridge Philos. Soc. 22 (1916), no. 9, 159-184.
|
19 |
Y. Simsek, Elliptic analogue of the Hardy sums related to elliptic Bernoulli functions, Gen. Math. 15 (2007), no. 3, 3-23.
|
20 |
H. M. Srivastava and A. Pinter, Remarks on some relationships between the Bernoulli and Euler polynomials, Appl. Math. Lett. 17 (2004), no. 4, 375-380.
DOI
ScienceOn
|
21 |
Z.-H. Sun, Congruences concerning Bernoulli numbers and Bernoulli polynomials, Discrete Appl. Math. 105 (2000), no. 1-3, 193-223.
DOI
ScienceOn
|
22 |
Z.-H. Sun, Legendre polynomials and supercongruences, Acta Arith. 159 (2013), no. 2, 169-200.
DOI
|
23 |
Z.-H. Sun, Congruences concerning Legendre polynomials. III, Int. J. Number Theory 9(2013), no. 4, 965-999.
DOI
ScienceOn
|
24 |
K. S. Williams, The convolution sum ${\Sigma}_{m
DOI
|
25 |
K. S. Williams, The parents of Jacobi's four squares theorem are unique, Amer. Math. Monthly 120 (2013), no. 4, 329-345.
DOI
ScienceOn
|
26 |
K. S. Williams, Number Theory in the Spirit of Liouville, London Mathematical Society, Student Texts 76, Cambridge, 2011.
|