具有密集值的格网

摘要：

给定一个从欧几里得空间到实数直线的连续函数，我们分析（在对函数的一些自然假设下）它在格上平移的值集。我们的结果是这样的：对于几乎任何翻译，值的集合在可能值的集合中是稠密的。结果，然后应用到各种具体的例子，获得新的信息在经典的讨论在不同领域的数学，特别是闵可夫斯基的猜想产品的非齐次形式和非齐次丢番图逼近。

英文摘要：

Given a continuous function from Euclidean space to the real line, we analyze (under some natural assumption on the function), the set of values it takes on translates of lattices. Our results are of the flavor: For almost any translate, the set of values is dense in the set of possible values. The results are then applied to a variety of concrete examples, obtaining new information in classical discussions in different areas in mathematics; in particular, Minkowski's conjecture regarding products of inhomogeneous forms and inhomogeneous Diophantine approximations.

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