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December 2016 Construction of class fields over cyclotomic fields
Ja Kyung Koo, Dong Sung Yoon
Kyoto J. Math. 56(4): 803-829 (December 2016). DOI: 10.1215/21562261-3664923

Abstract

Let and p be odd primes. For a positive integer μ, let kμ be the ray class field of k=Q(e2πi/) modulo 2pμ. We present certain class fields Kμ of k such that kμKμkμ+1, and we provide a necessary and sufficient condition for Kμ=kμ+1. We also construct, in the sense of Hilbert, primitive generators of the field Kμ over kμ by using Shimura’s reciprocity law and special values of theta constants.

Citation

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Ja Kyung Koo. Dong Sung Yoon. "Construction of class fields over cyclotomic fields." Kyoto J. Math. 56 (4) 803 - 829, December 2016. https://doi.org/10.1215/21562261-3664923

Information

Received: 31 August 2015; Revised: 26 October 2015; Accepted: 4 November 2015; Published: December 2016
First available in Project Euclid: 7 November 2016

zbMATH: 06663468
MathSciNet: MR3568642
Digital Object Identifier: 10.1215/21562261-3664923

Subjects:
Primary: 11F46, 11R37
Secondary: 11G15, 14H42

Rights: Copyright © 2016 Kyoto University

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Vol.56 • No. 4 • December 2016
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