椭球的格点计数器
Lattice-point enumerators of ellipsoids
摘要：
闵可夫斯基关于连续极小值的第二个定理断言，一个0-对称的凸体K在一个格Λ的余体积上的体积可以由一个包含K关于Λ的所有连续极小值的量来定界。我们将在这里证明，在K是椭球的特殊情况下，K内部的格点数目也可以接受大致相同大小的上界。这是否对所有K无条件也是正确的是一个开放的问题，但有合理的希望，用于椭球的归纳方法可以扩展到所有情况。
英文摘要：
Minkowski's second theorem on successive minima asserts that the volume of a 0-symmetric convex body K over the covolume of a lattice Λcan be bounded above by a quantity involving all the successive minima of K with respect to Λ. We will prove here that the number of lattice points inside K can also accept an upper bound of roughly the same size, in the special case where K is an ellipsoid. Whether this is also true for all K unconditionally is an open problem, but there is reasonable hope that the inductive approach used for ellipsoids could be extended to all cases.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
