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Elliot Benjamin

Publications and source records attributed to Elliot Benjamin.

7 recordsLinked to original sources
arXiv2026

On the Narrow 2-Class Field Tower of Some Real Quadratic Number Fields: Lengths Heuristics Follow-Up

In this article we continue the investigation of the length of the narrow $2$-class field tower of real quadratic number fields $\mathrm{k}$ whose discriminants are not a sum of two squares and for which their $2$-class groups are elementary of order $4$. Letting $\mathrm{G}$ equal the Galois group of the second Hilbert narrow $2$-class field over $\mathrm{k}$, and $[\mathrm{G}_i]$ denote the lower central series of $\mathrm{G}$, we give heuristic evidence that the length of the narrow $2$-class field tower of $\mathrm{k}$ is equal to $2$ when $\mathrm{G}/\mathrm{G}_3$ is of type $64.150$ (in the tables of Hall and Senior). We also give the formulation of the relevant unit groups of the narrow Hilbert $2$-class field for these fields.

math.NT↗
arXiv2025

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

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.

math.NT↗
arXiv2002

Imaginary quadratic fields with Cl_2(k) = (2,2,2)

In this article we classify the complex quadratic number fields k with 2-class group of type (2,2,2) whose Hilbert 2-class fields have a 2-class group of rank 2, and then determine the length of their 2-class field towers.

math.NT↗
arXiv2000

Imaginary quadratic fields k with Cl_2(k) = (2,2^m) and Rank Cl_2(k^1) = 2

We classify all complex quadratic number fields with 2-class group of type (2,2^m) whose Hilbert 2-class fields have class groups of 2-rank equal to 2. These fields all have 2-class field tower of length 2. We still don't know examples of fields with 2-class field tower of length 3, but the smallest candidate is the field with discriminant -1015.

math.NT↗