Galois number fields with small root discriminant
نویسندگان
چکیده
منابع مشابه
Number fields with solvable Galois groups and small Galois root discriminants
We apply class field theory to compute complete tables of number fields with Galois root discriminant less than 8πeγ . This includes all solvable Galois groups which appear in degree less than 10, groups of order less than 24, and all dihedral groups Dp where p is prime. Many people have studied questions of constructing complete lists of number fields subject to conditions on degree and possib...
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We enumerate all totally real number fields F with root discriminant δF ≤ 14. There are 1229 such fields, each with degree [F : Q] ≤ 9. In this article, we consider the following problem. Problem 1. Given B ∈ R>0, enumerate the set NF (B) of totally real number fields F with root discriminant δF ≤ B, up to isomorphism. To solve Problem 1, for each n ∈ Z>0 we enumerate the set NF (n,B) = {F ∈ NF...
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Let L/K be a Galois extension of number fields. We prove two lower bounds on the maximum of the degrees of the irreducible complex representations of Gal(L/K), the sharper of which is conditional on the Artin Conjecture and the Generalized Riemann Hypothesis. Our bound is nontrivial when [K : Q] is small and L has small root discriminant, and might be summarized as saying that such fields can’t...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2007
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2006.05.001