Thue equations associated with Ankeny-Brauer-Chowla number fields

Citation
F. Halter-koch et al., Thue equations associated with Ankeny-Brauer-Chowla number fields, J LOND MATH, 60, 1999, pp. 1-20
Citations number
18
Categorie Soggetti
Mathematics
Journal title
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES
ISSN journal
00246107 → ACNP
Volume
60
Year of publication
1999
Part
1
Pages
1 - 20
Database
ISI
SICI code
0024-6107(199908)60:<1:TEAWAN>2.0.ZU;2-2
Abstract
For a wide class of one-parameter families of Thue equations of arbitrary d egree n greater than or equal to 3 all solutions are determined if the para meter is sufficiently large. The result is based on the Lang-Waldschmidt co njecture, on the primitivity of the associated number fields and on an inde x bound, which does not depend on the coefficients. By applying the theory of Hilbertian fields and results on thin sets, primitivity is proved for al most all choices (in the sense of density) of the parameters.