The CM-fields with class number one which are Hilbert class fields of quadratic fields
نویسندگان
چکیده
منابع مشابه
CM-fields with relative class number one
We will show that the normal CM-fields with relative class number one are of degrees ≤ 216. Moreover, if we assume the Generalized Riemann Hypothesis, then the normal CM-fields with relative class number one are of degrees ≤ 96, and the CM-fields with class number one are of degrees ≤ 104. By many authors all normal CM-fields of degrees ≤ 96 with class number one are known except for the possib...
متن کاملComputation of Real Quadratic Fields with Class Number One
A rapid method for determining whether the real quadratic field Sí = S(\/D) has class number one is described. The method makes use of the infrastructure idea of Shanks to determine the regulator of .W and then uses the Generalized Riemann Hypothesis to rapidly estimate L(l, x) to the accuracy needed for determining whether or not the class number of 3£ is one. The results of running this algor...
متن کاملOne class genera of ternary quadratic forms over number fields
We enumerate all one class genera of definite ternary quadratic forms over number fields. For this, we construct all Gorenstein orders of type number one in definite quaternion algebras over number fields. Finally, we list all definite quaternion orders of ideal class number one.
متن کاملClass numbers of ray class fields of imaginary quadratic fields
Let K be an imaginary quadratic field with class number one and let p ⊂ OK be a degree one prime ideal of norm p not dividing 6dK . In this paper we generalize an algorithm of Schoof to compute the class numbers of ray class fields Kp heuristically. We achieve this by using elliptic units analytically constructed by Stark and the Galois action on them given by Shimura’s reciprocity law. We have...
متن کاملTernary quadratic forms over number fields with small class number
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.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the Japan Academy, Series A, Mathematical Sciences
سال: 1996
ISSN: 0386-2194
DOI: 10.3792/pjaa.72.16