On some theta constants and class fields

Ja Kyung Koo; Dong Hwa Shin

On some theta constants and class fields

Number Theory 2013-07-05 v2

Authors: Ja Kyung Koo , Dong Hwa Shin

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 certain theta constant by using Shimura's reciprocity law.

Keywords

siegel modular forms theta correspondence modular forms

Cite

@article{arxiv.1202.3213,
  title  = {On some theta constants and class fields},
  author = {Ja Kyung Koo and Dong Hwa Shin},
  journal= {arXiv preprint arXiv:1202.3213},
  year   = {2013}
}

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