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

2025/04/27 by Benjamin, Elliot, Snyder, C.
#11R29 #20D15 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2504.20785

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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