(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

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2022年 / 375卷 / 01期

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

页码：455 / 499

页数：45