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On some Fricke families and application to the Lang–Schertz conjecture

Part of: Arithmetic algebraic geometry Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  18 May 2016

Ho Yun Jung ,
Ja Kyung Koo  and
Dong Hwa Shin
Ho Yun Jung
Affiliation:
National Institute for Mathematical Sciences, Daejeon 305-811, Republic of Korea (hoyunjung@nims.re.kr)
Ja Kyung Koo
Affiliation:
Department of Mathematical Sciences, KAIST, Daejeon 305-701, Republic of Korea (jkkoo@math.kaist.ac.kr)
Dong Hwa Shin*
Affiliation:
Department of Mathematics, Hankuk University of Foreign Studies, Yongin-si, Gyeonggi-do 449-791, Republic of Korea (dhshin@hufs.ac.kr)
*
*Corresponding author.
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We investigate two kinds of Fricke families, those consisting of Fricke functions and those consisting of Siegel functions. In terms of their special values we then generate ray class fields of imaginary quadratic fields over the Hilbert class fields, which are related to the Lang–Schertz conjecture.

Keywords

complex multiplicationFricke familiesmodular functions

MSC classification

Secondary: 11G15: Complex multiplication and moduli of abelian varieties 11F03: Modular and automorphic functions
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 146 , Issue 4 , August 2016 , pp. 723 - 740
Copyright
Copyright © Royal Society of Edinburgh 2016