PENCILS OF NORM FORM EQUATIONS AND A CONJECTURE OF THOMAS

Abstract

We introduce a new method to deal with families of norm form equations. These generalize the Thue equations studied first by Thomas using Baker's Method (which, however, we do not use here). We show that for all large integer values of the parameter t, every solution over Z arises from specializing a solution over Z [ T ] by T = t . The results are completely effective.