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Density of Rational Points on diagonal bidegree ${(1,2)}$ hypersurface in ${\mathbb{P}^{{s}-1} \times \mathbb{P}^{{s}-1}}$
In this paper we establish an asymptotic formula for the number of rational points of bounded anticanonical height which lie on a certain Zariski dense subset of the biprojective hypersurface \begin{align*} x_1y_1^2+\ldots +x_sy_s^2 = 0\end{align*}in $\mathbb{P}^{s-1} \times \mathbb{P}^{s-1} $ with $s \geq 7$. This confirms the Manin conjecture for this …