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1. 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.
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
convolution sums, sum of divisors function, and theta functions
Language:
English
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.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public