Let $\Omega \subset \mathbb{R}^{d}$ be a convex body with everywhere positive curvature except at the origin and with the boundary $\partial \Omega$ as the graph 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 respect to translations and rotations of a dilated copy of the set $\Omega$.

中文翻译：

---

一个点为零曲率的凸集的差异

令 $\Omega \subset \mathbb{R}^{d}$ 是一个凸体，除了原点处处处都是正曲率，边界 $\partial \Omega$ 作为函数 $y=|x| 的图^{\gamma}$ 在具有 $\gamma \geq 2$ 的原点附近。我们考虑与集合 $\Omega$ 的扩展副本的平移和旋转有关的差异的 $L^{p}$ 范数。