East Asian mathematical journal

  • 제40권1호
  • /
  • Pages.95-107
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  • 2024
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  • 1226-6973(pISSN)
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  • 2287-2833(eISSN)
영남수학회 (The Youngnam Mathematical Society)
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ARTIN SYMBOLS OVER IMAGINARY QUADRATIC FIELDS

  • Dong Sung Yoon (Department of Mathematics Education Pusan National University)
  • 투고 : 2023.10.12
  • 심사 : 2024.01.23
  • 발행 : 2024.01.31
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초록

Let K be an imaginary quadratic field with ring of integers 𝓞K and N be a positive integer. By K(N) we mean the ray class field of K modulo N𝓞K. In this paper, for each prime p of K relatively prime to N𝓞K we explicitly describe the action of the Artin symbol (${\frac{K_{(N)}/K}{p}}$) on special values of modular functions of level N. Furthermore, we extend the Kronecker congruence relation for the elliptic modular function j to some modular functions of higher level.

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과제정보

This work was supported by a 2-Year Research Grant of Pusan National University.

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