82 research outputs found
Diophantine equations over global function fields I: The Thue equation
AbstractWe solve completely Thue equations in function fields over arbitrary finite fields. In the function field case such equations were formerly only solved over algebraically closed fields (of characteristic zero and positive characteristic). Our method can be applied to similar types of Diophantine equations, as well
On solving norm equations in global function fields
Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG geförderten) Allianz- bzw. Nationallizenz frei zugänglich.This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.The potential of solving norm equations is crucial for a variety of applications of algebraic number theory, especially in cryptography. In this article we develop general effective methods for that task in global function fields for the first time
Computation of 2-groups of positive classes of exceptional number fields
We present an algorithm for computing the 2-group of the positive divisor
classes of a number field F in case F has exceptional dyadic places. As an
application, we compute the 2-rank of the wild kernel WK2(F) in K2(F) for such
number fields
On computing integral points of a Mordell curve over rational function fields in characteristic >3
09221 Abstracts Collection -- Algorithms and NumberTheory
From 24.05. to 29.05.2009, the Dagstuhl Seminar 09221 ``Algorithms and Number Theory \u27\u27 was held in Schloss Dagstuhl~--~Leibniz Center for Informatics.
During the seminar, several participants presented their current
research, and ongoing work and open problems were discussed. Abstracts of
the presentations given during the seminar as well as abstracts of
seminar results and ideas are put together in this paper. The first section
describes the seminar topics and goals in general.
Links to extended abstracts or full papers are provided, if available
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