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On the number of representations of an integer by certain quadratic forms in sixteen variables
2014
International Journal of Number Theory
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We evaluate the convolution sums l,m∈N,l+2m=n σ3(l)σ3(m), l,m∈N,l+3m=n σ3(l)σ3(m), l,m∈N,2l+3m=n σ3(l)σ3(m) and l,m∈N,l+6m=n σ3(l)σ3(m) for all n ∈ N using the theory of modular forms and use these convolution sums to determine the number of representations of a positive integer n by the quadratic forms Q8 ⊕ Q8 and Q8 ⊕ 2Q8, where the quadratic form Q8 is given by
doi:10.1142/s1793042114500638
fatcat:4gschqraafacbey33wtmapedki