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arXiv · 1202.3213

On some theta constants and class fields

Ja Kyung Koo·Dong Hwa Shin
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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 certain theta constant by using Shimura's reciprocity law.

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Ja Kyung Koo, Dong Hwa Shin. 2012-02-15. On some theta constants and class fields. https://arxiv.org/abs/1202.3213

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