Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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THE RELATION PROPERTY BETWEEN THE DIVISOR FUNCTION AND INFINITE PRODUCT SUMS

  • 투고 : 2016.05.03
  • 심사 : 2016.07.01
  • 발행 : 2016.09.25
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초록

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 $L(q^4)D(q)$.

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참고문헌

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