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Arithmetic properties derived from coefficients of certain eta quotients
Journal of Inequalities and Applications ( IF 1.5 ) Pub Date : 2020-04-16 , DOI: 10.1186/s13660-020-02368-y
Jihyun Hwang , Yan Li , Daeyeoul Kim

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:

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)$。
更新日期:2020-04-18
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