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Siegel families with application to class fields

Part of: Arithmetic algebraic geometry Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  27 June 2018

Ja Kyung Koo ,
Dong Hwa Shin  and
Dong Sung Yoon
Ja Kyung Koo
Affiliation:
Department of Mathematical Sciences, KAIST, Daejeon 34141, Republic of Korea (jkkoo@math.kaist.ac.kr)
Dong Hwa Shin
Affiliation:
Department of Mathematics, Hankuk University of Foreign Studies, Yongin-si, Gyeonggi-do 17035, Republic of Korea (dhshin@hufs.ac.kr)
Dong Sung Yoon*
Affiliation:
Department of Mathematical Sciences, KAIST, Daejeon 34141, Republic of Korea
*
†Corresponding author.
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Abstract

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We investigate certain families of meromorphic Siegel modular functions on which Galois groups act in a natural way. By using Shimura's reciprocity law we construct some algebraic numbers in the ray class fields of CM-fields in terms of special values of functions in these Siegel families.

Keywords

abelian varietiesclass field theoryShimura's reciprocity lawCM-fieldsSiegel modular functions

MSC classification

Secondary: 11F46: Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms 11G15: Complex multiplication and moduli of abelian varieties
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 148 , Issue 4 , August 2018 , pp. 751 - 771
Copyright
Copyright © Royal Society of Edinburgh 2018 

Footnotes

*

Present address: Department of Mathematical Sciences, Ulsan National Institute of Science and Technology, Ulsan 44919, Republic of Korea (dsyoon@unist.ac.kr).