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On the Rational Points of the Curve $f(X,Y)^q = h(X)g(X,Y)$

  Published:2009-03-01
 Printed: Mar 2009
  • Dimitrios Poulakis
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Abstract

Let $q = 2,3$ and $f(X,Y)$, $g(X,Y)$, $h(X)$ be polynomials with integer coefficients. In this paper we deal with the curve $f(X,Y)^q = h(X)g(X,Y)$, and we show that under some favourable conditions it is possible to determine all of its rational points.
MSC Classifications: 11G30, 14G05, 14G25 show english descriptions Curves of arbitrary genus or genus $
Rational points
Global ground fields
11G30 - Curves of arbitrary genus or genus $
14G05 - Rational points
14G25 - Global ground fields
 

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