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arXiv · 2504.20785

On the Narrow $2$-Class Field Tower of Some Real Quadratic Number Fields, Part I: Ranks

Elliot Benjamin·C. Snyder
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Abstract

We determine some properties of the narrow 2-class field tower of those real quadratic number fields whose discriminants are not a sum of two squares and for which their 2-class groups are elementary of order $4$. Here in Part I, we determine precisely which of these fields have the 2-class groups of their narrow 2-Hilbert class fields of rank 2.

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Elliot Benjamin, C. Snyder. 2025-04-27. On the Narrow $2$-Class Field Tower of Some Real Quadratic Number Fields, Part I: Ranks. https://arxiv.org/abs/2504.20785

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