Ranks of 3-class groups of non-Galois cubic fields

Frank Gerth

Displaying similar documents to “Ranks of 3-class groups of non-Galois cubic fields”

On 3-class groups of non-Galois cubic fields

Kiyoaki Iimura (1979)

Acta Arithmetica

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Stark's conjecture in multi-quadratic extensions, revisited

David S. Dummit, Jonathan W. Sands, Brett Tangedal (2003)

Journal de théorie des nombres de Bordeaux

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Stark’s conjectures connect special units in number fields with special values of $L$ -functions attached to these fields. We consider the fundamental equality of Stark’s refined conjecture for the case of an abelian Galois group, and prove it when this group has exponent $2$ . For biquadratic extensions and most others, we prove more, establishing the conjecture in full.

On $2$ -class field towers of imaginary quadratic number fields

Franz Lemmermeyer (1994)

Journal de théorie des nombres de Bordeaux

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For a number field $k$ , let $k^{1}$ denote its Hilbert $2$ -class field, and put $k^{2} = {(k^{1})}^{1}$ . We will determine all imaginary quadratic number fields $k$ such that $G = G a l (k^{2} / k)$ is abelian or metacyclic, and we will give $G$ in terms of generators and relations.

On the 2-primary part of K₂ of rings of integers in certain quadratic number fields

A. Vazzana (1997)

Acta Arithmetica

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1. Introduction. For quadratic fields whose discriminant has few prime divisors, there are explicit formulas for the 4-rank of $K ₂_{E}$ . For quadratic fields whose discriminant has arbitrarily many prime divisors, the formulas are less explicit. In this paper we will study fields of the form $ℚ (\sqrt (p ₁ . . . p_{k}))$ , where the primes $p_{i}$ are all congruent to 1 mod 8. We will prove a theorem conjectured by Conner and Hurrelbrink which examines under what conditions the 4-rank of $K ₂_{E}$ is zero for such fields. In the course...