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Diophantine inequalities involving several power sums
Authors:Clemens?Fuchs  mailto:clemens.fuchs@tugraz.at"   title="  clemens.fuchs@tugraz.at"   itemprop="  email"   data-track="  click"   data-track-action="  Email author"   data-track-label="  "  >Email author,Amedeo?Scremin
Affiliation:(1) Technische Universität Graz, Institut für Mathematik, Steyrergasse 30/II, 8010 Graz, Austria;(2) Technische Universität Graz, Institut für Mathematik, Steyrergasse 30/II, 8010 Graz, Austria
Abstract:
Let MediaObjects/s00229-004-0486-5flb1.gif denote the ring of power sums, i.e. complex functions of the form MediaObjects/s00229-004-0486-5flb2.gif for some MediaObjects/s00229-004-0486-5flb3.gif and agrithinspisinthinspA, where MediaObjects/s00229-004-0486-5flb4.gif is a multiplicative semigroup. Moreover, let MediaObjects/s00229-004-0486-5flb5.gif We consider Diophantine inequalities of the form MediaObjects/s00229-004-0486-5flb6.gif where agr>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 MediaObjects/s00229-004-0486-5flb7.gif 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.Mathematics Subject Classification (2000):11D45,11D61Revised version: 6 May 2004
Keywords:
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