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.
Publié le : 2008-12-15
Classification:
Arithmetic graphs,
unit equations,
polynomials,
resultants,
discriminants,
diophantine finiteness theorems,
11D61,
11C08,
05C99
@article{1229696577,
author = {Gy\"ory, K\'alm\'an},
title = {On certain arithmetic graphs and their applications to diophantine problems},
journal = {Funct. Approx. Comment. Math.},
volume = {38},
number = {1},
year = {2008},
pages = { 289-314},
language = {en},
url = {http://dml.mathdoc.fr/item/1229696577}
}
Györy, Kálmán. On certain arithmetic graphs and their applications to diophantine problems. Funct. Approx. Comment. Math., Tome 38 (2008) no. 1, pp. 289-314. http://gdmltest.u-ga.fr/item/1229696577/