Evaluation of convolution sums ∑l+15m=nσ(l)σ(m) and ∑3l+5m=nσ(l)σ(m)

In this article, we have evaluated the convolution sums ∑ a l + b m = n σ ( l ) σ ( m ) for a · b = 15 , where a , b ∈ N , using an elementary method. The deduced convolution sums are in a little elegent form than that derived by B. Ramakrishnan and B. Sahu [ 24 ]. As a consequence, we determine a f...

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Bibliographic Details
Published in:Indian journal of pure and applied mathematics 2022, Vol.53 (4), p.1110-1121
Main Authors: Pushpa, K., Vasuki, K. R.
Format: Article
Language:English
Subjects:
Applications of Mathematics
Convolution
Mathematics
Mathematics and Statistics
Numerical Analysis
Original Research
Quadratic forms
Sums
Citations: Items that this one cites
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Summary:In this article, we have evaluated the convolution sums ∑ a l + b m = n σ ( l ) σ ( m ) for a · b = 15 , where a , b ∈ N , using an elementary method. The deduced convolution sums are in a little elegent form than that derived by B. Ramakrishnan and B. Sahu [ 24 ]. As a consequence, we determine a formula for the number of representations of a positive integer n by the octonary quadratic form x 1 2 + x 1 x 2 + x 2 2 + x 3 2 + x 3 x 4 + x 4 2 + 5 x 5 2 + x 5 x 6 + x 6 2 + x 7 2 + x 7 x 8 + x 8 2 .
ISSN:0019-5588
0975-7465
DOI:10.1007/s13226-022-00222-z