Densities for 4-class ranks of quadratic function fields
نویسندگان
چکیده
منابع مشابه
The 4-class Group of Real Quadratic Number Fields
In this paper we give an elementary proof of results on the structure of 4-class groups of real quadratic number fields originally due to A. Scholz. In a second (and independent) section we strengthen C. Maire’s result that the 2-class field tower of a real quadratic number field is infinite if its ideal class group has 4-rank ≥ 4, using a technique due to F. Hajir.
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The distribution of ideal class groups of Fq(T, √ M(T )) is examined for degree-four monic polynomials M ∈ Fq[T ] when Fq is a finite field of characteristic greater than 3 with q ∈ [20000, 100000] or q ∈ [1020000, 1100000] and M is irreducible or has an irreducible cubic factor. Particular attention is paid to the distribution of the p-Sylow part of the class group, and these results agree wit...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2009
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2009.03.004