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THUE EQUATIONS ASSOCIATED WITH ANKENY–BRAUER–CHOWLA NUMBER FIELDS

Published online by Cambridge University Press:  01 August 1999

F. HALTER-KOCH ,
G. LETTL ,
A. PETHŐ  and
R. F. TICHY
F. HALTER-KOCH
Affiliation:
Institut für Mathematik, Karl-Franzens-Universität Graz, Heinrichstraße 36, A-8010 Graz, Austria
G. LETTL
Affiliation:
Institut für Mathematik, Karl-Franzens-Universität Graz, Heinrichstraße 36, A-8010 Graz, Austria
A. PETHŐ
Affiliation:
Mathematical Institute, Kossuth Lajos University, PO Box 12, H-4010 Debrecen, Hungary
R. F. TICHY
Affiliation:
Institut für Mathematik, Technische Universität Graz, Steyrergasse 30, A-8010 Graz, Austria
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Abstract

For a wide class of one-parameter families of Thue equations of arbitrary degree n[ges ]3 all solutions are determined if the parameter is sufficiently large. The result is based on the Lang–Waldschmidt conjecture, on the primitivity of the associated number fields and on an index bound, which does not depend on the coefficients. By applying the theory of Hilbertian fields and results on thin sets, primitivity is proved for almost all choices (in the sense of density) of the parameters.

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 60 , Issue 1 , August 1999 , pp. 1 - 20
Copyright
The London Mathematical Society 1999

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