Arithmetic properties derived from coefficients of certain eta quotients.

For a positive integer k, let F (q) k : = ∏ n ≥ 1 (1 − q n) 4 k (1 + q 2 n) 2 k = ∑ n ≥ 0 a k (n) q n be the eta quotients. The coefficients a 1 (n) can be interpreted as a certain kind of restricted divisor sums. In this paper, we give the signs and modulo values for a 1 (n) and a 2 (m) and calculate several convolution sums involving a k (n) . [ABSTRACT FROM AUTHOR]

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