The Convolution Sum Σm<n/16σ(m)σ(n – 16m)
Canadian mathematical bulletin, Tome 51 (2008) no. 1, pp. 3-14
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The convolution sum $\sum{_{m is evaluated for all $n\,\in \,\mathbb{N}$ . This evaluation is used to determine the number of representations of $n$ by the quadratic form $x_{1}^{2}\,+\,x_{2}^{2}\,+\,x_{3}^{2}\,+\,x_{4}^{2}\,+\,4x_{5}^{2}\,+\,4x_{6}^{2}\,+\,4x_{7}^{2}\,+\,4x_{8}^{2}$ .
Mots-clés :
11A25, 11E20, 11E25, divisor functions, convolution sums, Eisenstein series
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S. The Convolution Sum Σm<n/16σ(m)σ(n – 16m). Canadian mathematical bulletin, Tome 51 (2008) no. 1, pp. 3-14. doi: 10.4153/CMB-2008-001-1
@article{10_4153_CMB_2008_001_1,
author = {Alaca, Ay\c{s}e and Alaca, \c{S}aban and Williams, Kenneth S.},
title = {The {Convolution} {Sum} {\ensuremath{\Sigma}m<n/16\ensuremath{\sigma}(m)\ensuremath{\sigma}(n} {\textendash} 16m)},
journal = {Canadian mathematical bulletin},
pages = {3--14},
year = {2008},
volume = {51},
number = {1},
doi = {10.4153/CMB-2008-001-1},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2008-001-1/}
}
TY - JOUR AU - Alaca, Ayşe AU - Alaca, Şaban AU - Williams, Kenneth S. TI - The Convolution Sum Σm<n/16σ(m)σ(n – 16m) JO - Canadian mathematical bulletin PY - 2008 SP - 3 EP - 14 VL - 51 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2008-001-1/ DO - 10.4153/CMB-2008-001-1 ID - 10_4153_CMB_2008_001_1 ER -
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