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Polynomial Bounds for the Solutions of a Class of Diophantine Equations

โœ Scribed by Dimitrios Poulakis

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
320 KB
Volume
66
Category
Article
ISSN
0022-314X

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โœฆ Synopsis

Let K be an algebraic number field such that all the embeddings of K into C are real. We denote by O K the ring of algebraic integers of K. Let F(X, Y) be an irreducible polynomial in K[X, Y ]&K[Y ] of total degree N and of degree n>0 in Y. We denote by F N (X, Y ) its leading homogeneous part. Suppose that F N (1, Y) is a polynomial of degree n having no real roots. In this paper we establish a polynomial upper bound for the size of solutions (x, y) # O K _K of the equation F(X, Y )=0.

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