Evaluation of the sums $\sum\limits_{\substack{m=1 \\ m\equiv a\pmod 4}}^{n-1} \sigma (m) \sigma (n-m)$.

Title:

Evaluation of the sums $\sum\limits_{\substack{m=1 \\ m\equiv a\pmod 4}}^{n-1} \sigma (m) \sigma (n-m)$.

Creator:

Alaca, Ayşe , Alaca, Şaban, and Williams, Kenneth S.

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:62065216-4a4d-4db5-85da-327d6edead04
uuid:62065216-4a4d-4db5-85da-327d6edead04

Subject:

convolution sums, sum of divisors function, and theta functions

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

The convolution sum $$ \sum\limits_{\substack{m=1 \\ m\equiv a\pmod 4}}^{n-1} \sigma (m) \sigma (n-m) $$ is evaluated for $a\in \{ 0,1,2,3\}$ and all $n \in \Bbb N$. This completes the partial evaluation given in the paper of J. G. Huard, Z. M. Ou, B. K. Spearman, K. S. Williams.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

847-859

Source:

Czechoslovak Mathematical Journal | 2009 Volume:59 | Number:3

Harvested from:

CDK

Metadata only:

false