Displaying similar documents to “Upper bounds for an Iwasawa invariant”

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.

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 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 ( √ ( 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...