On some theta constants and class fields

Details On some theta constants and class fields On some theta constants and class fields

2012-02-15

arxiv.org/abs/1202.3213v1

Mathematics

Number Theory

Scientific paper

We first find a necessary and 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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