Cyclotomic fields; Cyclotomic fields. II; Introduction to modular forms
نویسندگان
چکیده
منابع مشابه
Cyclotomic 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...
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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 کاملSparse Representation for Cyclotomic Fields
Currently, all major implementations of cyclotomic fields as well as number fields, are based on a dense model where elements are represented either as dense polynomials in the generator of the field or as coefficient vectors with respect to a fixed basis. While this representation allows for the asymptotically fastest arithmetic for general elements, it is unsuitable for fields of degree > 10 ...
متن کاملIdeal Class Groups of Cyclotomic Number Fields Ii
We first study some families of maximal real subfields of cyclotomic fields with even class number, and then explore the implications of large plus class numbers of cyclotomic fields. We also discuss capitulation of the minus part and the behaviour of p-class groups in cyclic ramified p-extensions. This is a continuation of [13]; parts I and II are independent, but will be used in part III. 6. ...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 1983
ISSN: 0001-8708
DOI: 10.1016/0001-8708(83)90065-8