Bernoulli numbers, convolution sums and congruences of coefficients for certain generating functions

被引:0
作者
Daeyeoul Kim
Aeran Kim
Ayyadurai Sankaranarayanan
机构
[1] National Institute for Mathematical Sciences,Department of Mathematics and Institute of Pure and Applied Mathematics
[2] Chonbuk National University,Permanent address: School of Mathematics
[3] Current address: National Institute for Mathematical Sciences,undefined
[4] Tata Institute of Fundamental Research,undefined
来源
Journal of Inequalities and Applications | / 2013卷
关键词
Bernoulli numbers; generating functions; divisor functions; convolution sums;
D O I
暂无
中图分类号
学科分类号
摘要
In this paper, we study the convolution sums involving restricted divisor functions, their generalizations, their relations to Bernoulli numbers, and some interesting applications.
引用
收藏
相关论文
共 20 条
[1]  
Ramanujan S(1916)On certain arithmetical functions Trans. Cambridge Philos. Soc 22 159-184
[2]  
Lahiri DB(1946)On Ramanujan’s function Bull. Calcutta Math. Soc 38 193-206
[3]  
Glaisher JWL(1885) and the divisor function Mess. Math 15 1-20
[4]  
Glaisher JWL(1884), I Mess. Math 14 156-163
[5]  
Glaisher JWL(1885)On certain sums of products of quantities depending upon the divisors of a number Mess. Math 15 33-36
[6]  
Hahn H(2007)On the square of the series in which the coefficients are the sums of the divisors of the exponents Rocky Mt. J. Math 37 1593-1622
[7]  
Lahiri DB(1947)Expressions for the five powers of the series in which the coefficients are the sums of the divisors of the exponents Bull. Calcutta Math. Soc 39 33-52
[8]  
Alaca S(2007)Convolution sums of some functions on divisors J. Number Theory 124 491-510
[9]  
Williams KS(2007)On Ramanujan’s function Gen. Math 15 3-23
[10]  
Simsek Y(2013) and the divisor function J. Math. Anal. Appl 397 522-528