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arXiv · 1203.4662

Construction of class fields over cyclotomic fields

Ja Kyung Koo·Dong Sung Yoon
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Abstract

Let $\ell$ and $p$ be odd primes. For a positive integer $\mu$ let $k_\mu$ be the ray class field of $k=\mathbb{Q}(e^{2\pi i/\ell})$ 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 we also construct, in the sense of Hilbert, primitive generators of the field $K_\mu$ over $k_\mu$ by using Shimura's reciprocity law and special values of theta constants.

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Ja Kyung Koo, Dong Sung Yoon. 2012-03-21. Construction of class fields over cyclotomic fields. https://doi.org/10.1215/21562261-3664923

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