Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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AVERAGE VALUES ON THE JACOBIAN VARIETY OF A HYPERELLIPTIC CURVE

  • Chung, Jiman (Department of Mathematics Chung-Ang University) ;
  • Im, Bo-Hae (Department of Mathematical Sciences KAIST)
  • Received : 2018.02.22
  • Accepted : 2018.10.25
  • Published : 2019.03.31
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Abstract

We give explicitly an average value formula under the multiplication-by-2 map for the x-coordinates of the 2-division points D on the Jacobian variety J(C) of a hyperelliptic curve C with genus g if $2D{\equiv}2P-2{\infty}$ (mod Pic(C)) for $P=(x_P,y_P){\in}C$ with $y_P{\neq}0$. Moreover, if g = 2, we give a more explicit formula for D such that $2D{\equiv}P-{\infty}$ (mod Pic(C)).

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Acknowledgement

Supported by : National Research Foundation of Korea(NRF)

References

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