On the Average Number of Rational Points on Curves of Genus 2
نویسنده
چکیده
The second part of this conjecture is analogous to Conjecture 2.2 (i) in [PV], which considers hypersurfaces in P. If C is a curve of genus 2 as above and P = (a : y : b) is a rational point on C (i.e., we have F (a, b) = y with a, b coprime integers), then we denote by H(P ) the height H(a : b) = max{|a|, |b|} of its x-coordinate. Conjecture 2. Let ε > 0. Then there is a constant Bε and a Zariski open subset Uε of the ‘coefficient space’ A such that for all C ∈ CN ∩ Uε and all rational points P on C, we have H(P ) ≤ BεN .
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