Class Number in Constant Extensions of 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 number approximation in cubic function fields

A central problem in number theory and algebraic geometry is the determination of the size of the group of rational points on the Jacobian of an algebraic curve over a finite field. This question also has applications to cryptography, since cryptographic systems based on algebraic curves generally require a Jacobian of non-smooth order in order to foil certain types of attacks. There a variety ...

متن کامل

Class number in totally imaginary extensions of totally real function fields

We show that, up to isomorphism, there are only finitely many totally real function fields which have any totally imaginary extension of a given ideal class number.

متن کامل

Class Number Growth of a Family of Z -Extensions p over Global Function Fields

Let F be a finite field with q elements and of characteristic p. In this q paper, we construct a family of geometric Z -extensions over global p function field k of transcendence degree one over F and study the q asymptotic behavior of class numbers in such Z -extensions. By the analog p of the Brauer]Siegel theorem in function fields, it suffices to investigate w x the genus of each layer of s...

متن کامل

Class numbers of some abelian extensions of rational function fields

Let P be a monic irreducible polynomial. In this paper we generalize the determinant formula for h(K Pn) of Bae and Kang and the formula for h−(KPn ) of Jung and Ahn to any subfields K of the cyclotomic function field KPn . By using these formulas, we calculate the class numbers h −(K), h(K+) of all subfields K of KP when q and deg(P ) are small.

متن کامل

Remark on infinite unramified extensions of number fields with class number one

We modify an idea of Maire to construct biquadratic number fields with small root discriminants, class number one, and having an infinite, necessarily non-solvable, strictly unramified Galois extension. Let k be an algebraic number field with class number one. Then k has no Abelian (and hence no solvable) non-trivial unramified Galois extension. It is somewhat surprising that k may nevertheless...

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: Proceedings of the American Mathematical Society

سال: 1972

ISSN: 0002-9939

DOI: 10.2307/2039035