逐次极小与格点

摘要：

本文的主要目的是证明中心对称凸体的格点个数的一个上界，它是由凸体的连续极小值表示的。这一界限提高了前界和缩小差距对一个晶格点模拟闵可夫斯基的第二定理连续极小。闵可夫斯基的证明，他的第二个定理是相当冗长，它也被批评为晦涩难懂。我们提出了一个简短的证明闵可夫斯基的第二定理连续极小值，这是基于闵可夫斯基的想法证明。

英文摘要：

The main purpose of this note is to prove an upper bound on the number of lattice points of a centrally symmetric convex body in terms of the successive minima of the body. This bound improves on former bounds and narrows the gap towards a lattice point analogue of Minkowski's second theorem on successive minima. Minkowski's proof of his second theorem is rather lengthy and it was also criticised as obscure. We present a short proof of Minkowski's second theorem on successive minima, which, however, is based on the ideas of Minkowski's proof.

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