Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2014; 51(6): 1269-1289

Printed November 1, 2014

https://doi.org/10.4134/JKMS.2014.51.6.1269

Copyright © The Korean Mathematical Society.

On some theta constants and class fields

Dong Hwa Shin

Hankuk University of Foreign Studies

Abstract

We first find a sufficient condition for a product of theta constants to be a Siegel modular function of a given even level. And, when $K_{(2p)}$ denotes the ray class field of $K=\mathbb{Q}(e^{2\pi i/5})$ modulo $2p$ for an odd prime $p$, we describe a subfield of $K_{(2p)}$ generated by the special value of a certain theta constant by using Shimura's reciprocity law.

Keywords: CM-fields, Shimura's reciprocity law, theta functions

MSC numbers: Primary 11F46; Secondary 11G15, 14K25

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