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http://dx.doi.org/10.5831/HMJ.2016.38.3.507

THE RELATION PROPERTY BETWEEN THE DIVISOR FUNCTION AND INFINITE PRODUCT SUMS  

Kim, Aeran (A Private mathematics academy)
Publication Information
Honam Mathematical Journal / v.38, no.3, 2016 , pp. 507-552 More about this Journal
Abstract
For a complex number q and a divisor function ${\sigma}_1(n)$ we define $$C(q):=q{\prod_{n=1}^{\infty}}(1-q^n)^{16}(1-q^{2n})^4,\\D(q):=q^2{\prod_{n=1}^{\infty}}(1-q^n)^8(1-q^{2n})^4(1-q^{4n})^8,\\L(q):=1-24{\sum_{n=1}^{\infty}}{\sigma}_1(n)q^n$$ moreover we obtain the number of representations of $n{\in}{\mathbb{N}}$ as sum of 24 squares, which are possible for us to deduce $L(q^4)C(q)$ and $L(q^4)D(q)$.
Keywords
divisor functions; infinite product sums;
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Times Cited By KSCI : 1  (Citation Analysis)
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