Indivisibility of class numbers of imaginary quadratic fields
نویسنده
چکیده
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 the number of imaginary quadratic fields with class number indivisible by a given prime. This general result is applied to study rank 0 twists of certain elliptic curves.
منابع مشابه
Indivisibility of Class Numbers of Imaginary Quadratic Fields and Orders of Tate-shafarevich Groups of Elliptic Curves with Complex Multiplication
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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