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December 2008 On certain arithmetic graphs and their applications to diophantine problems
Kálmán Györy
Funct. Approx. Comment. Math. 39(2): 289-314 (December 2008). DOI: 10.7169/facm/1229696577


In this paper we continue our investigations concerning arithmetic graphs associated with integral domains and their applications to diophantine problems. We establish some general quantitative theorems for these graphs considered over finitely generated integral domains and prove some effective analogues over number fields and function fields. Further, we apply our results to resultant equations and discriminant equations. In a separate paper, further applications will be given to decomposable form equations, algebraic numbers and irreducible polynomials.


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Kálmán Györy. "On certain arithmetic graphs and their applications to diophantine problems." Funct. Approx. Comment. Math. 39 (2) 289 - 314, December 2008.


Published: December 2008
First available in Project Euclid: 19 December 2008

zbMATH: 1226.11046
MathSciNet: MR2490742
Digital Object Identifier: 10.7169/facm/1229696577

Primary: 11C08 , 11D61
Secondary: 05C99

Keywords: Arithmetic graphs , diophantine finiteness theorems , discriminants , polynomials , resultants , unit equations

Rights: Copyright © 2008 Adam Mickiewicz University


Vol.39 • No. 2 • December 2008
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