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On the distribution of integer points of rational curves. (English) Zbl 1027.11022

Let \(F(X,Y)\in \mathbb{Z}[X,Y]\) be an absolutely irreducible polynomial. Recently, the authors gave a necessary and sufficient condition for the algebraic curve \(C:F(X,Y)=0\) to have infinitely many integer points [J. Symb. Comput. 33, 479-491 (2002; Zbl 0998.11014)]. In this paper the authors obtain an explicit estimate on the distribution of integer points of \(C\).

MSC:

11D41 Higher degree equations; Fermat’s equation
11G30 Curves of arbitrary genus or genus \(\ne 1\) over global fields
14H25 Arithmetic ground fields for curves
14H05 Algebraic functions and function fields in algebraic geometry

Citations:

Zbl 0998.11014
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