Evaluation of four convolution sums and representation of integers by certain quadratic forms in twelve variables

Bulent Kokluce

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).

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Published: 2022-01-10

How to Cite this Article:

Bulent Kokluce, Evaluation of four convolution sums and representation of integers by certain quadratic forms in twelve variables, J. Math. Comput. Sci., 12 (2022), Article ID 52

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.

 

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