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http://dx.doi.org/10.4134/JKMS.2015.52.5.907

GENERATION OF CLASS FIELDS BY SIEGEL-RAMACHANDRA INVARIANTS  

SHIN, DONG HWA (Department of Mathematics Hankuk University of Foreign Studies)
Publication Information
Journal of the Korean Mathematical Society / v.52, no.5, 2015 , pp. 907-928 More about this Journal
Abstract
We show in many cases that the Siegel-Ramachandra invariants generate the ray class fields over imaginary quadratic fields. As its application we revisit the class number one problem done by Heegner and Stark, and present a new proof by making use of inequality argument together with Shimura's reciprocity law.
Keywords
class field theory; complex multiplication; class numbers; elliptic and modular units; modular and automorphic functions;
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