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Fixed Point Theory and Algorithms for Sciences and Engineering

Table 3 Values of ∑ k = 1 N − 1 σ 1 ∗ ( 2 m k; 2 m ) σ 1 ∗ ( 2 m (N−k); 2 m )

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

∑ k = 1 N − 1 σ 1 ∗ (2k) σ 1 ∗ (2(N−k))

∑ k = 1 N − 1 σ 1 ∗ (4k;4) σ 1 ∗ (4(N−k);4)

⋯

∑ k = 1 N − 1 σ 1 ∗ ( 2 m k; 2 m ) σ 1 ∗ ( 2 m (N−k); 2 m )

( 2 − 1 ) 2 ( σ 3 ∗ (N)−N σ 1 ∗ (N))

( 4 − 1 ) 2 ( σ 3 ∗ (N)−N σ 1 ∗ (N))

⋯

( 2 m − 1 ) 2 ( σ 3 ∗ (N)−N σ 1 ∗ (N))

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