J Austral Math Soc Ser A 51 pp8--26, 1991.

Bounds for the Solutions of Some Diophantine Equations in Terms of Discriminants

B. Brindza, J. H. Evertse and K. Györy

Abstract

Several effective upper bounds are known for the solutions of Thue equations, Thue-Mahler equations and superelliptic equations. One of the basic parameters occuring in these bounds is the height of the polynomial involved in the equation. In the present paper it is shown that better (and, in certain important particular cases, best possible) upper bounds can be obtained in terms of the height, if one takes into consideration also the discriminant of the polynomial.

1980 AMS Subject Classification (1985 Revision): 11D41, 11D61

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Authors

B. Brindza

Mathematical Institute, Kossuth Lajos University, 4010 Debrecen, Hungary.

J. H. Evertse

K. Györy

Department of Mathematics and Computer Science, 2300 RA Leiden, P.O. Box 9512, The Netherlands.