[1] Points de hauteur bornĂ©e sur une surface de Del Pezzo (1993), 1—34
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let \(V\) be the Del Pezzo surface obtained
by blowing up three points in general position on the projective
plane. The aim of this text is to estimate the number of points
on \(V\) of bounded height which do not lie on exceptional
divisors. Manin had proven that this number should be equivalent
to \(CB\ln(B)^3\) for a constant \(C\).
Here we give an expression for \(C\) in terms of local densities
for \(V\), of the \(L\)-function of the Picard group of \(V\)
and the volume of some fundamental domain. Parts of the proof
generalize to an arbitrary number field.
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