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COMBINATORIC CONVOLUTION SUMS CONTAINING σ AND $\tilde{\sigma}$ OF THE FORM 2<sup>m</sup>p
Kim, Daeyeoul,Park, Joongsoo The Honam Mathematical Society 2014 호남수학학술지 Vol.36 No.3
In this paper, we study combinatoric convolution sums of divisor functions and get values of this sum when $n=2^mp$. We find that the value of this convolution sum is represented by a sum of powers of 2 and Bernoulli or Euler number.
A DIOPHANTINE PROBLEM CONCERNING POLYGONAL NUMBERS
KIM, DAEYEOUL,PARK, YOON KYUNG,PINTÉ,R, Á,KOS Cambridge University Press 2013 Bulletin of the Australian Mathematical Society Vol.88 No.2
<B>Abstract</B><P>Motivated by some earlier Diophantine works on triangular numbers by Ljunggren and Cassels, we consider similar problems for general polygonal numbers.</P>
ON THE CONVOLUTION SUMS OF CERTAIN RESTRICTED DIVISOR FUNCTIONS
Kim, Daeyeoul,Kim, Aeran,Sankaranarayanan, Ayyadurai The Honam Mathematical Society 2013 호남수학학술지 Vol.35 No.2
We study convolution sums of certain restricted divisor functions in detail and present explicit evaluations in terms of usual divisor functions for some specific situations.
REMARKS OF CONGRUENT ARITHMETIC SUMS OF THETA FUNCTIONS DERIVED FROM DIVISOR FUNCTIONS
Kim, Aeran,Kim, Daeyeoul,Ikikardes, Nazli Yildiz The Honam Mathematical Society 2013 호남수학학술지 Vol.35 No.3
In this paper, we study a distinction the two generating functions : ${\varphi}^k(q)=\sum_{n=0}^{\infty}r_k(n)q^n$ and ${\varphi}^{*,k}(q)={\varphi}^k(q)-{\varphi}^k(q^2)$ ($k$ = 2, 4, 6, 8, 10, 12, 16), where $r_k(n)$ is the number of representations of $n$ as the sum of $k$ squares. We also obtain some congruences of representation numbers and divisor function.
ARITHMETIC SUMS SUBJECT TO LINEAR AND CONGRUENT CONDITIONS AND SOME APPLICATIONS
Kim, Aeran,Kim, Daeyeoul,Sankaranarayanan, Ayyadurai The Honam Mathematical Society 2014 호남수학학술지 Vol.36 No.2
We investigate the explicit evaluation for the sum $\sum_{(a,b,x,y){\in}\mathbb{N}^4,\\{ax+by=n},\\{C(x,y)}$ ab in terms of various divisor functions (where C(x, y) is the set of residue conditions on x and y) for various fixed C(x, y). We also obtain some identities and congruences as interesting applications.