On some modular identities (original) (raw)
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In this paper, we study a distinction the two generating functions : ϕ k (q) = ∞ n=0 r k (n)q n and ϕ * ,k (q) = ϕ k (q) − ϕ k (q 2) (k = 2, 4, 6, 8, 10, 12, 16), where r k (n) is the number of representations of n as the sum of k squares. We also obtain some congruences of representation numbers and divisor function.