Construction of Class fields over cyclotomic fields

Details Construction of Class fields over cyclotomic fields Construction of Class fields over cyclotomic fields

2012-03-21

arxiv.org/abs/1203.4662v1

Mathematics

Number Theory

Scientific paper

Let $\ell$ and $p$ be odd primes. For a positive integer $\mu$ let $k_\mu$ be the ray class field of $k=\mathbb{Q}(e^\frac{2\pi i}{\ell})$ modulo $2p^\mu$. We present certain class fields $K_\mu$ of $k$ such that $k_\mu\leq K_\mu\leq k_{\mu+1}$, and find the degree of $K_\mu/k_\mu$ explicitly. And by using Shimura's reciprocity law we also construct generators of the field $K_\mu$ over $k_\mu$ in terms of special values of theta constants.

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