Ordinary cyclotomic function fields

نویسندگان

چکیده

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Class Numbers of Cyclotomic Function Fields

Let q be a prime power and let Fq be the nite eld with q elements. For each polynomial Q(T) in FqT ], one could use the Carlitz module to construct an abelian extension of Fq(T), called a Carlitz cyclotomic extension. Carlitz cyclotomic extensions play a fundamental role in the study of abelian extensions of Fq(T), similar to the role played by cyclotomic number elds for abelian extensions of Q...

متن کامل

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...

متن کامل

Classes 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 کامل

Diophantine 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 کامل

Sparse 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 کامل

ذخیره 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: Journal of Number Theory

سال: 2013

ISSN: 0022-314X

DOI: 10.1016/j.jnt.2012.08.008