# ON SOME RING CLASS FIELDS BY SHIMURA'S CANONICAL MODELS

• Choi, So-Young (DEPARTMENT OF MATHEMATICS EDUCATION DONGGUK UNIVERSITY) ;
• Koo, Ja-Kyung (KOREA ADVANCED INSTITUTE OF SCIENCE AND TECHNOLOGY DEPARTMENT OF MATHEMATICAL SCIENCES)
• Published : 2008.11.30

#### Abstract

We construct certain ring class fields over an imaginary quadratic field by making use of Shimura's canonical models and extend the result of Chen-Yui ([1] Theorem 3.7.5(2)) to the case where (a, b, N) $\neq$ N or (a/N, N) $\neq$ 1 for a positive integer N > 1.

#### References

1. I. Chen and N. Yui, Groups, Difference Sets and the Monster (OSU Math. Research Inst. Publication 4), 255-326, Walter de Gruyter & Co. 1995
2. J. H. Conway and S. P. Norton, Monstrous moonshine, Bull. London Math. Soc. 11 (1979), no. 3, 308-339 https://doi.org/10.1112/blms/11.3.308
3. H. Helling, Note uber das Geschlecht gewisser arithmetischer Gruppen, Math. Ann. 205 (1973), 173-179 https://doi.org/10.1007/BF01349227
4. C. H. Kim and J. K. Koo, Arithmetic of the modular function $j_{1,4}$, Acta Arith. 84 (1998), no. 2, 129-143 https://doi.org/10.4064/aa-84-2-129-143
5. S. Lang, Elliptic Functions, Springer-Verlag, 1987
6. G. Shimura, Introduction to the Arithmetic Theory of Automorphic Functions, Publications of the Mathematical Society of Japan, No. 11. Iwanami Shoten, Publishers, Tokyo; Princeton University Press, Princeton, N.J., 1971

#### Cited by

1. Singular values of principal moduli vol.133, pp.2, 2013, https://doi.org/10.1016/j.jnt.2012.08.006