Class number indivisibility for quadratic function fields
نویسندگان
چکیده
منابع مشابه
Indivisibility of Class Numbers of Real Quadratic Fields
Although the literature on class numbers of quadratic fields is quite extensive, very little is known. In this paper we consider class numbers of real quadratic fields, and as an immediate consequence we obtain an estimate for the number of vanishing Iwasawa λ invariants. Throughout D will denote the fundamental discriminant of the quadratic number fieldQ( √ D), h(D) its class number, and χD :=...
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We quantify a recent theorem of Wiles on class numbers of imaginary quadratic fields by proving an estimate for the number of negative fundamental discriminants down to −X whose class numbers are indivisible by a given prime and whose imaginary quadratic fields satisfy any given set of local conditions. This estimate matches the best results in the direction of the Cohen–Lenstra heuristics for ...
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We enumerate all positive definite ternary quadratic forms over number fields with class number at most 2. This is done by constructing all definite quaternion orders of type number at most 2 over number fields. Finally, we list all definite quaternion orders of ideal class number 1 or 2.
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because 2, 3, and 1± √ −5 are irreducible and nonassociate. These notes present a formula that in some sense measures the extent to which unique factorization fails in environments such as Z[ √ −5]. Algebra lets us define a group that measures the failure, geometry shows that the group is finite, and analysis yields the formula for its order. To move forward through the main storyline without b...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2010
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2010.05.003