自动序列实现了Sarnak猜想
Automatic sequences fulfill the Sarnak conjecture
摘要：
本文提出了一种处理自动序列的新方法。这种方法使我们能够证明一个莫比乌斯随机性原则的自动序列，从中我们推导出Sarnak猜想这类序列。此外，我们可以证明一个素数定理的自动序列所产生的强连接自动机的初态是固定的过渡对应于$0$。
英文摘要：
We present in this paper a new method to deal with automatic sequences. This method allows us to prove a Möbius-randomness-principle for automatic sequences from which we deduce the Sarnak conjecture for this class of sequences. Furthermore, we can show a Prime Number Theorem for automatic sequences that are generated by strongly connected automata where the initial state is fixed by the transition corresponding to $0$.
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。
