序列的幂与递归
Powers of sequences and recurrence
摘要：
我们研究递归，多个递归，沿$k$次幂的一组给定的整数的属性。我们证明了对于某些给定的$k$的值的递归的属性不给任何约束的递归的其他权力。这是由数论中关于自然数的加法基的类似结果激发的。此外，受Kamae和Mendès-France的一个结果的启发，将单次递归与序列的均匀分布性质联系起来，我们寻找了一个类似的结果来处理高阶递归，并提出了一个相关的猜想.
英文摘要：
We study recurrence, and multiple recurrence, properties along the $k$-th powers of a given set of integers. We show that the property of recurrence for some given values of $k$ does not give any constraint on the recurrence for the other powers. This is motivated by similar results in number theory concerning additive basis of natural numbers. Moreover, motivated by a result of Kamae and Mendès-France, that links single recurrence with uniform distribution properties of sequences, we look for an analogous result dealing with higher order recurrence and make a related conjecture.
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