For a positive integer k, let $$ F (q)^{k}:= \prod_{n \geq 1} \frac{(1-q^{n})^{4k}}{(1+q^{2n})^{2k}} = \sum_{n\geq 0} \frak{a}_{k} (n)q^{n} $$ be the eta quotients. The coefficients $\frak{a}_{1} (n)$ can be interpreted as a certain kind of restricted divisor sums. In this paper, we give the signs and modulo values for $\frak{a}_{1} (n)$ and $\frak{a}_{2} (m)$ and calculate several convolution sums involving $\frak{a}_{k} (n)$.

中文翻译：

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从某些η商的系数得出的算术性质

对于正整数k，令$$ F（q）^ {k}：= \ prod_ {n \ geq 1} \ frac {（1-q ^ {n}）^ {4k}} {（1 + q ^ {2n}）^ {2k}} = \ sum_ {n \ geq 0} \ frak {a} _ {k}（n）q ^ {n} $$是eta商。系数$ \ frak {a} _ {1}（n）$可以解释为某种限制的除数和。在本文中，我们给出$ \ frak {a} _ {1}（n）$和$ \ frak {a} _ {2}（m）$的符号和模值，并计算涉及$ \ frak的几个卷积和{a} _ {k}（n）$。