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J. Korean Math. Soc. 2018; 55(1): 131-146
Online first article June 15, 2017 Printed January 1, 2018
https://doi.org/10.4134/JKMS.j170079
Copyright © The Korean Mathematical Society.
Generation of ring class fields by eta-quotients
Ja Kyung Koo, Dong Hwa Shin, Dong Sung Yoon
KAIST, Hankuk University of Foreign Studies, KAIST
We generate ring class fields of imaginary quadratic fields in terms of the special values of certain eta-quotients, which are related to the relative norms of Siegel-Ramachandra invariants. These give us minimal polynomials with relatively small coefficients from which we are able to solve certain quadratic Diophantine equations concerning non-convenient numbers.
Keywords: class field theory, complex multiplication, elliptic and modular units
MSC numbers: Primary 11G16; Secondary 11F03, 11G15, 11R37
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