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Table 6 Special cases of convolution sums

From: Convolution identities for twisted Eisenstein series and twisted divisor functions

Convolution sums

Convolution sums

m = 1 L σ 1 (2m1) σ 1 (2L2m+1)= σ 3 (L)

m = 1 L σ 1 (2m1) σ 3 (2L2m+1)= σ 5 (L)

m = 1 2 L 1 ( 1 ) m + 1 σ 1 (m) σ 1 (2Lm)=L σ 1 (L)

m = 1 2 L 1 ( 1 ) m + 1 σ 1 (m) σ 3 (2Lm)=L σ 3 (L)