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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The Diophantine equation $ \alpha _{1}^{x_{1}}\cdots \alpha _{n}^{x_{n}} = f(x_{1},\dots ,x_{n})$. II


Authors: P. Corvaja, W. M. Schmidt and U. Zannier
Journal: Trans. Amer. Math. Soc. 362 (2010), 2115-2123
MSC (2000): Primary 11D61, 11D45; Secondary 11R18
Published electronically: November 18, 2009
MathSciNet review: 2574889
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Abstract: We will deal with the equation of the title where $ \alpha _{1},\dots ,\alpha _{n}$ are multiplicatively independent complex numbers and $ f$ is a polynomial. We will give a bound for the number of solutions which depends only on $ n$ and the degree of $ f$. Two further results which play a rôle in the proof are of independent interest.


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Additional Information

P. Corvaja
Affiliation: Department of Mathematics and Informatics, University of Udine, Via delle Scienze 206, 33100 Udine, Italy

W. M. Schmidt
Affiliation: Department of Mathematics, University of Colorado at Boulder, Boulder, Colorado 80309-0395

U. Zannier
Affiliation: Department of Mathematics, Scuola Normale Superiore, Piazza de Cavalier, 56100 Pisa, Italy

DOI: http://dx.doi.org/10.1090/S0002-9947-09-05012-0
PII: S 0002-9947(09)05012-0
Received by editor(s): May 13, 2008
Published electronically: November 18, 2009
Article copyright: © Copyright 2009 American Mathematical Society