Indivisibility of class numbers of global 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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Let q be a prime power and let Fq be the nite eld with q elements. For each polynomial Q(T) in FqT ], one could use the Carlitz module to construct an abelian extension of Fq(T), called a Carlitz cyclotomic extension. Carlitz cyclotomic extensions play a fundamental role in the study of abelian extensions of Fq(T), similar to the role played by cyclotomic number elds for abelian extensions of Q...
متن کاملClass numbers of some abelian extensions of rational function fields
Let P be a monic irreducible polynomial. In this paper we generalize the determinant formula for h(K Pn) of Bae and Kang and the formula for h−(KPn ) of Jung and Ahn to any subfields K of the cyclotomic function field KPn . By using these formulas, we calculate the class numbers h −(K), h(K+) of all subfields K of KP when q and deg(P ) are small.
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Since Gauss, ideal class groups of imaginary quadratic fields have been the focus of many investigations, and recently there have been many investigations regarding TateShafarevich groups of elliptic curves. In both cases the literature is quite extensive, but little is known. Throughout D will denote a fundamental discriminant of a quadratic field. Let CL(D) denote the class group of Q( √ D), ...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 2009
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa138-3-4