# Diophantine inequalities involving several power sums

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## Abstract.

Let Open image in new window denote the ring of power sums, i.e. complex functions of the form Open image in new window for some Open image in new window and *α*_{ i } ∈ *A*, where Open image in new window is a multiplicative semigroup. Moreover, let Open image in new window We consider Diophantine inequalities of the form Open image in new window 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 Open image in new window 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.

## Keywords

Complex Function Multiplicative Semigroup Diophantine Inequality Dominant Root## Preview

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## Notes

### 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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