HILBERT 2-CLASS FIELD TOWERS OF REAL QUADRATIC FUNCTION FIELDS
نویسندگان
چکیده
منابع مشابه
On 2-class field towers of imaginary quadratic number fields
For a number field k, let k1 denote its Hilbert 2-class field, and put k2 = (k1)1. We will determine all imaginary quadratic number fields k such that G = Gal(k2/k) is abelian or metacyclic, and we will give G in terms of generators and relations.
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Using the units appearing in Stark’s conjectures on the values of L-functions at s = 0, we give a complete algorithm for computing an explicit generator of the Hilbert class field of a real quadratic field. Let k be a real quadratic field of discriminant dk, so that k = Q( √ dk), and let ω denote an algebraic integer such that the ring of integers of k is Ok := Z+ ωZ. An important invariant of ...
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Weuse a result of Y. Furuta to show that for almost all positive integers m, the cyclotomic field (exp(2π i/m)) has an infinite Hilbert p-class field tower with high rankGalois groups at each step, simultaneously for all primes p of size up to about (log logm)1+o(1). We also use a recent result of B. Schmidt to show that for infinitely many m there is an infinite Hilbert p-class field tower ove...
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We determine all real quadratic number fields with 2-class field tower of length at most 1.
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We construct an infinite family of imaginary quadratic number fields with 2-class groups of type (2, 2, 2) whose Hilbert 2-class fields are finite.
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ژورنال
عنوان ژورنال: Communications of the Korean Mathematical Society
سال: 2014
ISSN: 1225-1763
DOI: 10.4134/ckms.2014.29.2.219