A note on divisor class groups of degree zero of algebraic function fields over finite fields

Date

2003-01-01

Author

Özbudak, Ferruh

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

88
views

0
downloads

We give tight upper bounds on the number of degree one places of an algebraic function field over a finite field in terms of the exponent of a natural subgroup of the divisor class group of degree zero.. (C) 2002 Elsevier Science (USA). All rights reserved.

Subject Keywords

Theoretical Computer Science, General Engineering, Algebra and Number Theory, Applied Mathematics

URI

https://hdl.handle.net/11511/34690

Journal

FINITE FIELDS AND THEIR APPLICATIONS

DOI

https://doi.org/10.1016/s1071-5797(02)00004-7

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

Curves with many points and configurations of hyperplanes over finite fields Özbudak, Ferruh (Elsevier BV, 1999-10-01) We establish a correspondence between a class of Kummer extensions of the rational function field and configurations of hyperplanes in an affine space. Using this correspondence, we obtain explicit curves over finite fields with many rational points. Some of our examples almost attain the Oesterle bound. (C) 1999 Academic Press.
ON FINITE GALOIS STABLE ARITHMETIC GROUPS AND THEIR APPLICATIONS Khrebtova, Ekaterina S.; Malinin, Dmitry (World Scientific Pub Co Pte Lt, 2008-12-01) We prove the existence and finiteness theorems for integral representations stable under Galois operation. An explicit construction of the realization fields for representations of finite groups stable under the natural operation of the Galois group is given. We also compare the representations over fields and the rings of integers, and give a quantitative result on the rarity of integral Galois stable representations. There is a series of related conjectures and applications to arithmetic algebraic geometr...
Value sets of Lattes maps over finite fields Küçüksakallı, Ömer (Elsevier BV, 2014-10-01) We give an alternative computation of the value sets of Dickson polynomials over finite fields by using a singular cubic curve. Our method is not only simpler but also it can be generalized to the non-singular elliptic case. We determine the value sets of Lattes maps over finite fields which are rational functions induced by isogenies of elliptic curves with complex multiplication.
CLASS NUMBERS OF RAY CLASS FIELDS OF IMAGINARY QUADRATIC FIELDS Küçüksakallı, Ömer (American Mathematical Society (AMS), 2011-04-01) Let K be an imaginary quadratic field with class number one and let p subset of O(K) be a degree one prime ideal of norm p not dividing 6d(K). In this paper we generalize an algorithm of Schoof to compute the class numbers of ray class fields K(p) heuristically. We achieve this by using elliptic units analytically constructed by Stark and the Galois action on them given by Shimura's reciprocity law. We have discovered a very interesting phenomenon where p divides the class number of K(p). This is a countere...
A note on b-weakly compact operators Alpay, Safak; Altin, Birol (Springer Science and Business Media LLC, 2007-11-01) We consider a continuous operator T : E -> X where E is a Banach lattice and X is a Banach space. We characterize the b-weak compactness of T in terms of its mapping properties.

Citation Formats

F. Özbudak, “A note on divisor class groups of degree zero of algebraic function fields over finite fields,” FINITE FIELDS AND THEIR APPLICATIONS, pp. 129–133, 2003, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/34690.