Simple families of Thue inequalities

Authors:
Günter Lettl, Attila Petho and Paul Voutier

Journal:
Trans. Amer. Math. Soc. **351** (1999), 1871-1894

MSC (1991):
Primary 11J25, 11J82; Secondary 11D25, 11D41

DOI:
https://doi.org/10.1090/S0002-9947-99-02244-8

Published electronically:
January 26, 1999

MathSciNet review:
1487624

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Abstract | References | Similar Articles | Additional Information

Abstract: We use the hypergeometric method to solve three families of Thue inequalities of degree 3, 4 and 6, respectively, each of which is parametrized by an integral parameter. We obtain bounds for the solutions, which are astonishingly small compared to similar results which use estimates of linear forms in logarithms.

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Additional Information

**Günter Lettl**

Affiliation:
Institut für Mathematik, Karl-Franzens-Universität, Heinrichstraße 36, A-8010 Graz, Austria

Email:
guenter.lettl@kfunigraz.ac.at

**Attila Petho**

Affiliation:
Department of Mathematics and Informatics, Lajos Kossuth University, P.O. Box 12, H-4010 Debrecen, Hungary

Email:
pethoe@math.klte.hu

**Paul Voutier**

Affiliation:
Department of Mathematics, University of Colorado, Boulder, Colorado 80309

Address at time of publication:
Optrak Distribution Software Ltd., Cawthorne House, 51 St. Andrew Street, Hertford SG14 1HZ, Great Britain

Email:
paul@optrak.co.uk

DOI:
https://doi.org/10.1090/S0002-9947-99-02244-8

Received by editor(s):
March 31, 1997

Published electronically:
January 26, 1999

Additional Notes:
Research of the first author was supported by the Hungarian-Austrian governmental scientific and technological cooperation.

Research of the second author was supported by the Hungarian National Foundation for Scientific Research Grant No. 16791/95.

Article copyright:
© Copyright 1999
American Mathematical Society