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CONGRUENCES OF THE WEIERSTRASS ${\wp}(x)$ AND ${\wp}^{{\prime}{\prime}}(x)$($x=\frac{1}{2}$, $\frac{\tau}{2}$, $\frac{\tau+1}{2}$)-FUNCTIONS ON DIVISORS

  • Kim, Daeyeoul (National Institute for Mathematical Sciences) ;
  • Kim, Aeran (Department of Mathematics and Institute of Pure and Applied Mathematics Chonbuk National University) ;
  • Park, Hwasin (Department of Mathematics and Institute of Pure and Applied Mathematics Chonbuk National University)
  • Received : 2011.07.25
  • Published : 2013.01.31
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Abstract

In this paper, we find the coefficients for the Weierstrass ${\wp}(x)$ and ${\wp}^{{\prime}{\prime}}(x)$($x=\frac{1}{2}$, $\frac{\tau}{2}$, $\frac{\tau+1}{2}$)-functions in terms of the arithmetic identities appearing in divisor functions which are proved by Ramanujan ([23]). Finally, we reprove congruences for the functions ${\mu}(n)$ and ${\nu}(n)$ in Hahn's article [11, Theorems 6.1 and 6.2].

Keywords

References

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