Functiones et Approximatio Commentarii Mathematici

On certain arithmetic graphs and their applications to diophantine problems

Kálmán Györy

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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.

Article information

Funct. Approx. Comment. Math., Volume 39, Number 2 (2008), 289-314.

First available in Project Euclid: 19 December 2008

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11D61: Exponential equations 11C08: Polynomials [See also 13F20]
Secondary: 05C99: None of the above, but in this section

Arithmetic graphs unit equations polynomials resultants discriminants diophantine finiteness theorems


Györy, Kálmán. On certain arithmetic graphs and their applications to diophantine problems. Funct. Approx. Comment. Math. 39 (2008), no. 2, 289--314. doi:10.7169/facm/1229696577.

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