Poincaré institute

Reinventing rational points

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Counting rational points of cubic hypersurfaces

Per Salberger

Let \(N(X;B)\) be the number of rational points of height at most \(B\) on an integral cubic hypersurface \(X\) over \(\mathbf Q\). It is then a central problem in Diophantine geometry to study the asymptotic behavior of \(N(X;B)\) when \(B\) growths. We present some recent results on this for various classes of cubic hypersurfaces.