IJPAM: Volume 53, No. 3 (2009)
DIOPHANTINE EQUATIONS OVER GLOBAL FUNCTION
FIELDS V: RESULTANT EQUATIONS IN
TWO UNKNOWN POLYNOMIALS
FIELDS V: RESULTANT EQUATIONS IN
TWO UNKNOWN POLYNOMIALS
István Gaál
, Michael Pohst
Mathematical Institute
University of Debrecen
Debrecen Pf. 12., H-4010, HUNGARY
e-mail: igaal@math.klte.hu
Institut für Mathematik
Technische Universität Berlin
136, Straße des 17. Juni, Berlin, GERMANY
e-mail: pohst@math.tu-berlin.de
, Michael Pohst
Mathematical Institute
University of Debrecen
Debrecen Pf. 12., H-4010, HUNGARY
e-mail: igaal@math.klte.hu
Institut für Mathematik
Technische Universität Berlin
136, Straße des 17. Juni, Berlin, GERMANY
e-mail: pohst@math.tu-berlin.de
Abstract.We give an efficient algorithm to solve resultant type equations in two unknown polynomials over global function fields. The method is based on the complete resolution of unit equations in three variables over function fields. This is the first time when such equations are completely solved.
Received: April 20, 2009
AMS Subject Classification: 11D57, 11Y50
Key Words and Phrases: global function fields, unit equations, resultant type equations
Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 53
Issue: 3