• Title/Summary/Keyword: Artin symbols

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ARTIN SYMBOLS OVER IMAGINARY QUADRATIC FIELDS

  • Dong Sung Yoon
    • East Asian mathematical journal
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    • v.40 no.1
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    • pp.95-107
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    • 2024
  • 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.