Exceptional units and Euclidean number fields
نویسندگان
چکیده
منابع مشابه
Exceptional units in a family of quartic number fields
We determine all exceptional units among the elements of certain groups of units in quartic number fields. These groups arise from a oneparameter family of polynomials with two real roots.
متن کاملChebyshev Covers and Exceptional Number Fields
Among the simplest of the classical polynomials are the Chebyshev polynomials of the first and second kind, Tk(x) and Uk(x). In our normalization, the indices are allowed to be halfintegers as well as integers, and the “polynomials” actually live in Z[x, √ 2− x, √ 2 + x]. We will show that the rational functions Tm/2(x) Tn/2(x) and Um/2(x) Un/2(x) are very remarkable from the point of view of G...
متن کاملÉtale Wild Kernels of Exceptional Number Fields
We clarify the relationship between higher étale wild kernels of a number field at the prime 2 and the Galois-coinvariants of Tate-twisted class groups in the 2cyclotomic tower of the field. We also determine the relationship between the étale wild kernel and the group of infinitely divisible elements of H(F, Z2(j + 1)){2}.
متن کاملRecognizing Units in Number Fields
We present a deterministic polynomial-time algorithm that decides whether a power product n¿=i ff is a umt m tne ring of integers of K , where K isa number field, y, are nonzero elements of K and n¡ are rational integers. The main algorithm is based on the factor refinement method for ideals, which might be of independent interest.
متن کاملThe Euclidean Algorithm in Cubic Number Fields
In this note we present algorithms for computing Euclidean minima of cubic number fields; in particular, we were able to find all normEuclidean cubic number fields with discriminants −999 < d < 104.
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: Archiv der Mathematik
سال: 2007
ISSN: 0003-889X,1420-8938
DOI: 10.1007/s00013-006-1019-0