Functiones et Approximatio Commentarii Mathematici

On certain arithmetic graphs and their applications to diophantine problems

Kálmán Györy

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Abstract

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

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

Dates
First available in Project Euclid: 19 December 2008

Permanent link to this document
https://projecteuclid.org/euclid.facm/1229696577

Digital Object Identifier
doi:10.7169/facm/1229696577

Mathematical Reviews number (MathSciNet)
MR2490742

Zentralblatt MATH identifier
1226.11046

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

Keywords
Arithmetic graphs unit equations polynomials resultants discriminants diophantine finiteness theorems

Citation

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. https://projecteuclid.org/euclid.facm/1229696577


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