The Distribution of Prime Ideals of Imaginary Quadratic Fields
نویسنده
چکیده
منابع مشابه
Real and imaginary quadratic representations of hyperelliptic function fields
A hyperelliptic function field can be always be represented as a real quadratic extension of the rational function field. If at least one of the rational prime divisors is rational over the field of constants, then it also can be represented as an imaginary quadratic extension of the rational function field. The arithmetic in the divisor class group can be realized in the second case by Cantor’...
متن کاملIndivisibility of class numbers of imaginary quadratic fields
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 ...
متن کاملSTATISTICS OF K-GROUPS MODULO p FOR THE RING OF INTEGERS OF A VARYING QUADRATIC NUMBER FIELD
For each odd prime p, we conjecture the distribution of the p-torsion subgroup of K2n(OF ) as F ranges over real quadratic fields, or over imaginary quadratic fields. We then prove that the average size of the 3-torsion subgroup of K2n(OF ) is as predicted by this conjecture.
متن کاملEuclidean Ideals in Quadratic Imaginary Fields
— We classify all quadratic imaginary number fields that have a Euclidean ideal class. There are seven of them, they are of class number at most two, and in each case the unique class that generates the class-group is moreover norm-Euclidean.
متن کاملEuclidean Ideals in Quadratic
— We classify all quadratic imaginary number fields that have a Euclidean ideal class. There are seven of them, they are of class number at most two, and in each case the unique class that generates the class-group is moreover norm-Euclidean.
متن کامل