Realizability of representations in cyclotomic fields
نویسندگان
چکیده
منابع مشابه
Irreducible representations and Artin L-functions of quasi-cyclotomic fields
We determine all irreducible representations of primary quasi-cyclotomic fields in this paper. The methods can be applied to determine the irreducible representations of any quasi-cyclotomic field. We also compute the Artin L-functions for a class of quasi-cyclotomic fields.
متن کاملCyclotomic Fields
Cyclotomic fields are an interesting laboratory for algebraic number theory because they are connected to fundamental problems Fermat’s Last Theorem for example and also have relatively simple algebraic properties that makes them an excellent laboratory for results in algebraic number theory. I will assume that you are familiar with basic algebraic number theory. Namely, the unique factorizatio...
متن کاملClasses of Cyclotomic Fields
As one will see in n◦4, these two theorems are deduced from a structure theorem for a certain group of operators. This group is constructed thus: let Xn be the p-component of the ideal class group of Kn; it is a finite abelian p-group, of order p en , which is acted opon by the Galois group G(Kn/Q) and in particular its subgroup Γn = G(Kn/K0). In passing to the projective limit over n with the ...
متن کاملDiophantine Equations in Cyclotomic Fields
where p is a given rational prime? It is almost trivial (from the theory of the Gaussian sum or otherwise) that a solution exists with g =p; it is less trivial that a solution also exists when g = p+p+l; but it is not asserted that solutions do not exist for other values of g. While we are unable to give anything like a complete answer to the problem proposed, we can prove something in this dir...
متن کاملIsotropic Realizability of Current Fields in ℝ3
This paper deals with the isotropic realizability of a given regular divergence free field j in R3 as a current field, namely to know when j can be written as σ∇u for some isotropic conductivity σ > 0, and some gradient field ∇u. The local isotropic realizability in R3 is obtained by Frobenius’ theorem provided that j and curl j are orthogonal in R3. A counter-example shows that Frobenius’ cond...
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 American Mathematical Society
سال: 1973
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1973-0314954-9