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Let $\Omega \subset \mathbb{R}^{d}$ be a convex body with everywhere positivecurvature except at the origin and with the boundary $\partial \Omega$ as thegraph of the function $y=|x|^{\gamma}$ in a neighborhood of the origin with$\gamma \geq 2$. We consider the $L^{p}$ norm of the discrepancy with respectto translations and rotations of a dilated copy of the set $\Omega$.

Discrepancy of a convex set with zero curvature at one point