Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
권호 표지
DOI QR코드

DOI QR Code

GALOIS ACTIONS OF A CLASS INVARIANT OVER QUADRATIC NUMBER FIELDS WITH DISCRIMINANT D ≡ 21 (mod 36)

  • Jeon, Daeyeol (Department of Mathematics Education Kongju National University)
  • Received : 2011.10.21
  • Accepted : 2011.12.02
  • Published : 2011.12.30
Download PDF
⟨ Previous Next ⟩

Abstract

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 a class invariant from a generalized Weber function $g_2$ over quadratic number fields with discriminant $D{\equiv}21$ (mod 36).

Keywords

Acknowledgement

Supported by : National Research Foundation of Korea(NRF)

References

  1. H. H. Chan, A. Gee and V. Tan, Cubic singular moduli, Ramanujan's class invariants ${\lambda}_n$ and the explicit Shimura reciprocity law, Pacific J. Math. 208 (2003), 23-37. https://doi.org/10.2140/pjm.2003.208.23
  2. A. Gee, Class invariants by Shimura's reciprocity law, J. Theor. Nombre Bordeaux 11 (1999), 45-72. https://doi.org/10.5802/jtnb.238
  3. A. Gee, Class fields by Shimura reciprocity, Ph. D. Thesis, Universiteit van Amsterdam, 2001.
  4. D. Jeon, C. H. Kim and S.-Y. Kang, Modularity of Galois traces of class invariants, to appear in Math. Ann.
  5. H. Weber, Lehrbuch der Algebra, dritter Band, Friedrich Vieweg und Sohn, 1908.