Evaluation of four convolution sums and representation of integers by certain quadratic forms in twelve variables
Abstract
In this paper the convolution sums ∑6i+j=n σ(l)σ3(m), ∑2i+3j=n σ(l)σ3(m), ∑i+6j=n σ(l)σ3(m) and ∑3i+2j=n σ(l)σ3(m) are evaluated for all n∈N, and then their evaluations are used to determine the representation number formulae N(1,1,1,1,1,2;n),N(1,1,1,1,2,2;n) and N(1,1,1,2,2,2;n) where N(a1,...,a6;n) denote the representation numbers of n by the form a1(x21 + x1x2 + x22) + a2(x23 + x3x4 + x24 ) + a3(x25 + x5x6 + x26) + a4(x27 + x7x8 +x28 ) +a5(x29 +x9x10 +x210) +a6(x211 +x11x12 +x212).
Copyright © 2022 Bulent Kokluce. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Cite this article
B. Kokluce, Evaluation of four convolution sums and representation of integers by certain quadratic forms in twelve variables, J. Math. Comput. Sci. 12 (2022), 52. https://doi.org/10.28919/jmcs/7016
BibTeX
@article{Kokluce2022,
author = {Kokluce, Bulent},
title = {Evaluation of four convolution sums and representation of integers by certain quadratic forms in twelve variables},
journal = {J. Math. Comput. Sci.},
volume = {12},
year = {2022},
pages = {52},
doi = {10.28919/jmcs/7016}
}