论文标题
（对数）沿素数和正方形的自动序列的密度
(Logarithmic) densities for automatic sequences along primes and squares
论文作者
论文摘要
在本文中，我们开发了一种将原始自动序列的密度结果传递到一般自动序列的对数密度结果的方法。作为一个应用程序，我们表明，沿正方形$（n^2）_ {n \ geq 0} $和primes $（p_n）_ {n \ geq 1} $的对数密度的对数密度（n^2）_ {n \ geq 0} $都存在并且可计算。此外，我们为这些子序列提供了一个标准来决定是否存在密度，在这种情况下它们也是可计算的。 特别是在主要情况下，这些密度都是理性的。我们还从第三作者和莱曼奇克的最新结果中得出，自动序列生成的所有子迁移均与任何有限的乘法性静脉函数正交。
In this paper we develop a method to transfer density results for primitive automatic sequences to logarithmic-density results for general automatic sequences. As an application we show that the logarithmic densities of any automatic sequence along squares $(n^2)_{n\geq 0}$ and primes $(p_n)_{n\geq 1}$ exist and are computable. Furthermore, we give for these subsequences a criterion to decide whether the densities exist, in which case they are also computable. In particular in the prime case these densities are all rational. We also deduce from a recent result of the third author and Lemańczyk that all subshifts generated by automatic sequences are orthogonal to any bounded multiplicative aperiodic function.
