Upper bounds for the number of number fields with alternating Galois group
نویسندگان
چکیده
منابع مشابه
Upper Bounds for the Number of Number Fields with Alternating Galois Group
We study the number N(n,An, X) of number fields of degree n whose Galois closure has Galois group An and whose discriminant is bounded by X. By a conjecture of Malle, we expect that N(n,An, X) ∼ Cn ·X 1 2 ·(logX)bn for constants bn and Cn. For 6 ≤ n ≤ 84393, the best known upper bound is N(n,An, X) � X n+2 4 ; this bound follows from Schmidt’s Theorem, which implies there are � X n+2 4 number f...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2012
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-2012-11543-6