Abstract.
Let 
denote the ring of power sums, i.e. complex functions of the form 
for some 
and α
i
∈ A, where 
is a multiplicative semigroup. Moreover, let 
We consider Diophantine inequalities of the form 
where α>1 is a quantity depending on the dominant roots of the power sums appearing as coefficients in F(n,y), and show that all its solutions 
have y parametrized by some power sums from a finite set. This is a continuation of the work of Corvaja and Zannier [4–6] and of the authors [10, 18] on such problems.
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Acknowledgments.
The first author was supported by the Austrian Science Foundation FWF, grant S8307-MAT. The second author was supported by Istituto Nazionale di Alta Matematica “Francesco Severi”, grant for abroad Ph.D. Both authors are most grateful to an anonymous referee for careful reading of the text and for several useful remarks improving previous versions of the paper.
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Mathematics Subject Classification (2000):11D45,11D61
Revised version: 6 May 2004
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Fuchs, C., Scremin, A. Diophantine inequalities involving several power sums. manuscripta math. 115, 163–178 (2004). https://doi.org/10.1007/s00229-004-0486-5
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DOI: https://doi.org/10.1007/s00229-004-0486-5