(LOGARITHMIC) DENSITIES FOR AUTOMATIC SEQUENCES ALONG PRIMES AND SQUARES

被引:1
作者
Adamczewski, Boris [1 ]
Drmota, Michael
Muellner, Clemens
机构
[1] Univ Lyon, Univ Claude Bernard Lyon 1, CNRS, UMR 5208,Inst Camille Jordan, 43 Blvd 11 Novembre 1918, F-69622 Villeurbanne, France
基金
欧洲研究理事会;
关键词
Automatic sequences; logarithmic density; primes; squares; FULFILL; DIGITS; SUM;
D O I
10.1090/tran/8476
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
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 >= 0) and primes (p(n))(n >= 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 Lemanczyk that all subshifts generated by automatic sequences are orthogonal to any bounded multiplicative aperiodic function.
引用
收藏
页码:455 / 499
页数:45
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