[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/JKMS.j170220

GENERATION OF RAY CLASS FIELDS MODULO 2, 3, 4 OR 6 BY USING THE WEBER FUNCTION

Jung, Ho Yun (Applied Algebra and Optimization Research Center Sungkyunkwan University)
Koo, Ja Kyung (Department of Mathematical Sciences KAIST)
Shin, Dong Hwa (Department of Mathematics Hankuk University of Foreign Studies)

Publication Information

Journal of the Korean Mathematical Society / v.55, no.2, 2018 , pp. 343-372 More about this Journal

Abstract

Let K be an imaginary quadratic field with ring of integers ${\mathcal{O}}_K$ . Let E be an elliptic curve with complex multiplication by ${\mathcal{O}}_K$ , and let $h_E$ be the Weber function on E. Let $N{\in}\{2,3,4,6\}$ . We show that $h_E$ alone when evaluated at a certain N-torsion point on E generates the ray class field of K modulo $N{\mathcal{O}}_K$ . This would be a partial answer to the question raised by Hasse and Ramachandra.

Keywords

class field theory; complex multiplication; Weber function;

Citations & Related Records

Reference

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