충청수학회지 (Journal of the Chungcheong Mathematical Society)

  • 제22권4호
  • /
  • Pages.799-814
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  • 2009
  • /
  • 1226-3524(pISSN)
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  • 2383-6245(eISSN)
충청수학회 (The Chungcheong Mathematical Society)
권호 표지

FORMULAS OF GALOIS ACTIONS OF SOME CLASS INVARIANTS OVER QUADRATIC NUMBER FIELDS WITH DISCRIMINANT D ≡ 1(mod 12)

  • Jeon, Daeyeol (Department of Mathematics Education, Kongju National University)
  • 투고 : 2009.10.06
  • 심사 : 2009.11.11
  • 발행 : 2009.12.30
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초록

A class invariant is the value of a modular function that generates a ring class field of an imaginary quadratic number field such as the singular moduli of level 1. In this paper, using Shimura Reciprocity Law, we compute the Galois actions of some class invariants from the generalized Weber functions $\mathfrak{g}_0,\mathfrak{g}_1,\mathfrak{g}_2$ and $\mathfrak{g}_3$ over quadratic number fields with discriminant $D{\equiv}1$ (mod 12).

키워드

참고문헌

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