Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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ON SOME THETA CONSTANTS AND CLASS FIELDS

  • Shin, Dong Hwa (Department of Mathematics Hankuk University of Foreign Studies)
  • Received : 2014.03.13
  • Published : 2014.11.01
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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

Acknowledgement

Supported by : NRF

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