Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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GENERATION OF RAY CLASS FIELDS MODULO 2, 3, 4 OR 6 BY USING THE WEBER FUNCTION

  • Jung, Ho Yun (Applied Algebra and Optimization Research Center Sungkyunkwan University) ;
  • Koo, Ja Kyung (Department of Mathematical Sciences KAIST) ;
  • Shin, Dong Hwa (Department of Mathematics Hankuk University of Foreign Studies)
  • Received : 2017.03.30
  • Accepted : 2017.09.05
  • Published : 2018.03.01
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Abstract

Let K be an imaginary quadratic field with ring of integers ${\mathcal{O}}_K$. Let E be an elliptic curve with complex multiplication by ${\mathcal{O}}_K$, and let $h_E$ be the Weber function on E. Let $N{\in}\{2,3,4,6\}$. We show that $h_E$ alone when evaluated at a certain N-torsion point on E generates the ray class field of K modulo $N{\mathcal{O}}_K$. This would be a partial answer to the question raised by Hasse and Ramachandra.

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Acknowledgement

Supported by : National Research Foundation of Korea (NRF), Hankuk University of Foreign Studies

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