Displaying similar documents to “The size function h 0 for quadratic number fields”

Unramified quaternion extensions of quadratic number fields

Franz Lemmermeyer (1997)

Journal de théorie des nombres de Bordeaux

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Classical results of Rédei, Reichardt and Scholz show that unramified cyclic quartic extensions of quadratic number fields k correspond to certain factorizations of its discriminant disc k . In this paper we extend their results to unramified quaternion extensions of k which are normal over ℚ , and show how to construct them explicitly.

On integral representations by totally positive ternary quadratic forms

Elise Björkholdt (2000)

Journal de théorie des nombres de Bordeaux

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Let K be a totally real algebraic number field whose ring of integers R is a principal ideal domain. Let f ( x 1 , x 2 , x 3 ) be a totally definite ternary quadratic form with coefficients in R . We shall study representations of totally positive elements N ∈ R by f . We prove a quantitative formula relating the number of representations of N by different classes in the genus of f to the class number of R [ - c f N ] , where c f ∈ R is a constant depending only on f . We give an algebraic proof of a classical result of H. Maass...

Maximal unramified extensions of imaginary quadratic number fields of small conductors

Ken Yamamura (1997)

Journal de théorie des nombres de Bordeaux

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We determine the structures of the Galois groups Gal ( K u r / K ) of the maximal unramified extensions K u r of imaginary quadratic number fields K of conductors ≦ 420 ( ≦ 719 under the Generalized Riemann Hypothesis). For all such K , K u r is K , the Hilbert class field of K , the second Hilbert class field of K , or the third Hilbert class field of K . The use of Odlyzko’s discriminant bounds and information on the structure of class groups obtained by using the action of Galois groups on class groups is essential. We...