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.
|Number of pages||26|
|Journal||Functiones et Approximatio, Commentarii Mathematici|
|Publication status||Published - 2008|
- Arithmetic graphs
- Diophantine finiteness theorems
- Unit equations
ASJC Scopus subject areas