Geodesic
Some applications of decomposable form equations to resultant equations
Colloquium Mathematicum, Tome 65 (1993) no. 2, pp. 267-275.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

1. Introduction. The purpose of this paper is to establish some general finiteness results (cf. Theorems 1 and 2) for resultant equations over an arbitrary finitely generated integral domain R over ℤ. Our Theorems 1 and 2 improve and generalize some results of Wirsing [25], Fujiwara [6], Schmidt [21] and Schlickewei [17] concerning resultant equations over ℤ. Theorems 1 and 2 are consequences of a finiteness result (cf. Theorem 3) on decomposable form equations over R. Some applications of Theorems 1 and 2 are also presented to polynomials in R[X] assuming unit values at many given points in R (cf. Corollary 1) and to arithmetic progressions of given order, consisting of units of R (cf. Corollary 2). Further applications to irreducible polynomials will be given in a separate paper. Our Theorem 3 seems to be interesting in itself as well. It is deduced from some general results of Evertse and the author [3] on decomposable form equations. Since the proofs in [3] depend among other things on the Thue-Siegel-Roth-Schmidt method and its p-adic generalization
DOI : 10.4064/cm-65-2-267-275

K. Győry 1

1 
@article{10_4064_cm_65_2_267_275,
     author = {K. Gy\H{o}ry},
     title = {Some applications of decomposable form equations to resultant equations},
     journal = {Colloquium Mathematicum},
     pages = {267--275},
     publisher = {mathdoc},
     volume = {65},
     number = {2},
     year = {1993},
     doi = {10.4064/cm-65-2-267-275},
     language = {fr},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/cm-65-2-267-275/}
}
TY  - JOUR
AU  - K. Győry
TI  - Some applications of decomposable form equations to resultant equations
JO  - Colloquium Mathematicum
PY  - 1993
SP  - 267
EP  - 275
VL  - 65
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/cm-65-2-267-275/
DO  - 10.4064/cm-65-2-267-275
LA  - fr
ID  - 10_4064_cm_65_2_267_275
ER  - 
%0 Journal Article
%A K. Győry
%T Some applications of decomposable form equations to resultant equations
%J Colloquium Mathematicum
%D 1993
%P 267-275
%V 65
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/cm-65-2-267-275/
%R 10.4064/cm-65-2-267-275
%G fr
%F 10_4064_cm_65_2_267_275
K. Győry. Some applications of decomposable form equations to resultant equations. Colloquium Mathematicum, Tome 65 (1993) no. 2, pp. 267-275. doi : 10.4064/cm-65-2-267-275. http://geodesic.mathdoc.fr/articles/10.4064/cm-65-2-267-275/

Cité par Sources :