The multinomial convolution sums of certain divisor functions

Bumkyu Cho; Daeyeoul Kim; Ho Park

doi:10.1016/j.jmaa.2016.11.052

The multinomial convolution sums of certain divisor functions

Bumkyu Cho
, Daeyeoul Kim^*
, Ho Park

^*Corresponding author for this work

Department of Mathematics

Dongguk University
National Institute for Mathematical Sciences

Research output: Contribution to journal › Journal article › peer-review

6 Scopus citations

Abstract

In this article we first introduce some results about the binomial, trinomial, and quadrinomial convolution sums of certain divisor functions and then we provide an identity for the multinomial convolution sums of the divisor function σ_r ^♯(n):=∑_{d|nn/d≡1(4)}d^r−(−1)^r∑_{d|nn/d≡−1(4)}d^r.

Original language	English
Pages (from-to)	1163-1174
Number of pages	12
Journal	Journal of Mathematical Analysis and Applications
Volume	448
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2016.11.052
State	Published - 2017.04.15

Keywords

Convolution sums
Divisor functions

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10.1016/j.jmaa.2016.11.052

Cite this

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title = "The multinomial convolution sums of certain divisor functions",

abstract = "In this article we first introduce some results about the binomial, trinomial, and quadrinomial convolution sums of certain divisor functions and then we provide an identity for the multinomial convolution sums of the divisor function σr ♯(n):=∑d|nn/d≡1(4)dr−(−1)r∑d|nn/d≡−1(4)dr.",

keywords = "Convolution sums, Divisor functions",

author = "Bumkyu Cho and Daeyeoul Kim and Ho Park",

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T1 - The multinomial convolution sums of certain divisor functions

AU - Cho, Bumkyu

AU - Kim, Daeyeoul

AU - Park, Ho

PY - 2017/4/15

Y1 - 2017/4/15

N2 - In this article we first introduce some results about the binomial, trinomial, and quadrinomial convolution sums of certain divisor functions and then we provide an identity for the multinomial convolution sums of the divisor function σr ♯(n):=∑d|nn/d≡1(4)dr−(−1)r∑d|nn/d≡−1(4)dr.

AB - In this article we first introduce some results about the binomial, trinomial, and quadrinomial convolution sums of certain divisor functions and then we provide an identity for the multinomial convolution sums of the divisor function σr ♯(n):=∑d|nn/d≡1(4)dr−(−1)r∑d|nn/d≡−1(4)dr.

KW - Convolution sums

KW - Divisor functions

UR - https://www.scopus.com/pages/publications/85006160527

U2 - 10.1016/j.jmaa.2016.11.052

DO - 10.1016/j.jmaa.2016.11.052

M3 - Journal article

AN - SCOPUS:85006160527

SN - 0022-247X

VL - 448

SP - 1163

EP - 1174

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

The multinomial convolution sums of certain divisor functions

Abstract

Keywords

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