边界为平点的旋转体晶格不一致的均方界
A mean-square bound for the lattice discrepancy of bodies of rotation with flat points on the boundary
摘要：
设B表示相对于一个坐标轴的三维旋转体，其边界足够光滑，并且除了旋转轴上的两个边界点之外，其余都具有有界的非零高斯曲率，在这两个边界点处曲率可能为零。对于一个大的实变量t，我们感兴趣的是线性扩张体tB中的整数点的数目A（t），特别是在晶格差异P（t）= A（t）-体积（tB）中。我们能够评估曲率为零的边界点对P（t）的贡献，其余数在均方上相当小。
英文摘要：
Let B denote a three-dimensional body of rotation, with respect to one coordinate axis, whose boundary is sufficiently smooth and of bounded nonzero Gaussian curvature throughout, except for the two boundary points on the axis of rotation, where the curvature may vanish. For a large real variable t, we are interested in the number A(t) of integer points in the linearly dilated body tB, in particular in the lattice discrepancy P(t) = A(t) - volume(tB). We are able to evaluate the contribution of the boundary points of curvature zero to P(t), with a remainder that is fairly small in mean-square.
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