在具有包含孤立平坦点的光滑边界的大凸体中计数整数点通常是球（或具有处处具有正曲率的光滑边界的凸体）和立方体（或凸多胞体）之间的中间情况。在本文中，我们提供了一个详细的描述，在特定的平面的情况下，边界局部重合的功能$\mathbb{R\ni}t\mapsto\left\vert t\right\vert ^γ$，与$γ>2$的图形的几个差异问题。我们考虑\textit{integer points}问题和\textit{irregularities of distribution}问题。上述\textquotedblleft对特定凸体族的限制\textquotedblright \被许多证明是初等的事实所补偿。该文件是完全独立的。
英文摘要：
Counting integer points in large convex bodies with smooth boundaries containing isolated flat points is oftentimes an intermediate case between balls (or convex bodies with smooth boundaries having everywhere positive curvature) and cubes (or convex polytopes). In this paper we provide a detailed description of several discrepancy problems in the particular planar case where the boundary coincides locally with the graph of the function $\mathbb{R\ni}t\mapsto\left\vert t\right\vert ^γ$, with $γ>2$. We consider both \textit{integer points} problems and \textit{irregularities of distribution} problems. The above \textquotedblleft restriction\textquotedblright\ to a particular family of convex bodies is compensated by the fact that many proofs are elementary. The paper is entirely self-contained.
Analytic van der Corput Lemma for p-adic and F_q((t)) oscillatory integrals, singular Fourier transforms, and restriction theorems
本文给出了实vanderCorput引理的p-adic和F_q（（t））模拟，其中相位充分光滑的实条件被相位是收敛的幂级数的条件所取代。这个van der Corput风格的结果，使我们能够在类比的真实情况下，研究奇异的傅里叶变换适当弯曲（解析）流形，并开辟了道路，为进一步的应用。作为这样的进一步应用，我们给出了L^p函数到非阿基米德局部域上适当弯曲的解析流形的傅里叶变换的限制定理，类似于E. Stein和C.弗利曼。
