The determination of all imaginary, quartic, abelian number fields with class number $1$
نویسندگان
چکیده
منابع مشابه
Class Numbers of Imaginary Abelian Number Fields
Let N be an imaginary abelian number field. We know that hN , the relative class number of N , goes to infinity as fN , the conductor of N , approaches infinity, so that there are only finitely many imaginary abelian number fields with given relative class number. First of all, we have found all imaginary abelian number fields with relative class number one: there are exactly 302 such fields. I...
متن کاملThe Determination of the Imaginary Abelian Number Fields with Class Number One
In this paper, we determine all the imaginary abelian number fields with class number one. There exist exactly 172 imaginary abelian number fields with class number one. The maximal conductor of these fields is 10921 = 67 • 163 , which is the conductor of the biquadratic number field Q(\/-67, v'—163).
متن کاملComputation of Relative Class Numbers of Imaginary Abelian Number Fields
Mathematics Subject Classi cation: Primary, 11R20, 11R29, 11Y40; Secondary, 11M20, 11R42.
متن کاملDetermination of All Nonquadratic Imaginary Cyclic Number Fields of 2-power Degrees with Ideal Class Groups of Exponents
We determine all nonquadratic imaginary cyclic number fields K of 2-power degrees with ideal class groups of exponents < 2, i.e., with ideal class groups such that the square of each ideal class is the principal class, i.e., such that the ideal class groups are isomorphic to some (Z/2Z)m , m > 0. There are 38 such number fields: 33 of them are quartic ones (see Theorem 13), 4 of them are octic ...
متن کاملRelative class number of imaginary Abelian fields of prime conductor below 10000
In this paper we compute the relative class number of all imaginary Abelian fields of prime conductor below 10000. Our approach is based on a novel multiple evaluation technique, and, assuming the ERH, it has a running time of O(p2 log(p) log log(p)), where p is the conductor of the field.
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: Mathematics of Computation
سال: 1980
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-1980-0583516-2