Evaluation of the sums \(\displaystyle\sum_{m=1\atop m\equiv a\pmod 4}^{n-1} \sigma (m) \sigma (n-m) \). (English) Zbl 1204.11009

Summary: The convolution sum \(\displaystyle\sum_{m=1\atop m\equiv a\pmod 4}^{n-1}\sigma(m)\sigma(n-m)\) is evaluated for \(a\in\{ 0,1,2,3\}\) and all \(n\in\mathbb N\). This completes the partial evaluation given in the paper of J. G. Huard, Z. M. Ou, B. K. Spearman and K. S. Williams [Number theory for the millennium II. Proceedings of the millennial conference on number theory, Urbana-Champaign, IL, USA, 2000. Natick, MA: A. K. Peters, 229–274 (2002; Zbl 1062.11005)].


11A25 Arithmetic functions; related numbers; inversion formulas
11F27 Theta series; Weil representation; theta correspondences


Zbl 1062.11005
Full Text: DOI EuDML


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