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March 2015 Imaginary quadratic fields with 2-class group of type $(2,2^\ell)$
Adele Lopez
Funct. Approx. Comment. Math. 52(1): 37-55 (March 2015). DOI: 10.7169/facm/2015.52.1.3

Abstract

We prove that for any given positive integer $\ell$ there are infinitely many imaginary quadratic fields with 2-class group of type $(2,2^\ell)$, and provide a lower bound for the number of such groups with bounded discriminant for $\ell\ge2$. This work is based on a related result for cyclic 2-class groups by Dominguez, Miller and Wong, and our proof proceeds similarly. Our proof requires introducing congruence conditions into Perelli's result on Goldbach numbers represented by polynomials, which we establitish in some generality.

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Adele Lopez. "Imaginary quadratic fields with 2-class group of type $(2,2^\ell)$." Funct. Approx. Comment. Math. 52 (1) 37 - 55, March 2015. https://doi.org/10.7169/facm/2015.52.1.3

Information

Published: March 2015
First available in Project Euclid: 20 March 2015

zbMATH: 06425011
MathSciNet: MR3326122
Digital Object Identifier: 10.7169/facm/2015.52.1.3

Subjects:
Primary: 11R29
Secondary: 11P32

Rights: Copyright © 2015 Adam Mickiewicz University

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Vol.52 • No. 1 • March 2015
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